Speculation on things shown in RWBY. I haven't read much behind the scenes information so this is mostly analyzing based on what I've seen.
It's hard to pinpoint exactly what Ozpin is doing or who he really is. We know that he's combating a secret war that the "brotherhood" want to keep from the public to prevent panic. Songs like Divide have lines implied to be directed at Ozpin blaming him for the lives lost on his side. Some of his actions have been questioned in the show while others haven't really been addressed yet.
How old is Ozpin ? He tells Pyrrha that the story of the Maidens has been around since he was a boy which she laughs off saying he's not that old. Some of the lines Salem says do seem to hint there's more to him. World of Remnant: Aura suggests he's "more than a man." Let's not forget that all the names were supposed to have connections to color which was a trend started after the war eighty years. Ozpin doesn't have a name related to a color so wouldn't that imply he was older ?
Chess has been a common theme between Ozpin and his enemies. When Cinder hacks into the system the Queen symbol appears, he uses chess pieces for the relics he sets out for the student entrance exam. He always seems to be plotting and this has caused friction especially since he doesn't always share his information. While most of his colleagues trust his judgement he does keep them in the dark. Qrow might know more than most but General Ironwood couldn't stand being kept out of the loop. He saw it as Ozpin not trusting him and the lack off action as being too passive. Not all Ozpin's actions turned out quite right though. Sending team RWBY on a mission didn't prevent the city from being attacked and the Council took away his power over the tournament. He has admitted to Ruby that he's made more mistakes than any man, woman or child but are some of these choices cruel?
Ozpin seems like a positive role model at times that's willing to bend the rules. Showing some tender moments with Ruby and Blake for example. He truly seems to see the need to let his students be kids while they can and knows they can't be protected from the upcoming war. Yet he does have some questionable actions. How far is too far? While choosing Pyrrha for the Fall Maiden was arguably morally wrong due to Ambers' condition it seemed like the only option. It was a desperate move, one Ozpin seemed to regret and even refused to go through with until Pyrrha verbally agreed.
Allowing Ruby to go to Beacon two years early--likely because of her being a silver eyed warrior--seems like another stroke of his master plan. He has shown interest in her success but even when he helps her out there's nothing extreme. Ozpin knew her team was going to look into finding the White Fang regardless of what their assignment was so he agreed to help. RWBY were the ones who took on the Torchwick outside school grounds. They like Pyrrha at least had some training and skill before he decided to bring them into his plans. What other actions has he done that might make us ponder how far he's willing to go to achieve his goals? Well it starts with one question:
How much does he know about Jaune Arc ?
This has never been crystal clear as the two don't share many interactions. This one out of all of Ozpin's actions bothers me the most. There are implications that Ozpin knows the truth of Jaune entering Beacon with fake transcripts. For the sake of this entry we'll be assuming he does. When Glynda notes Jaune partnering up with Pyrrha it's the only time during the entrance exam that Ozpin looks up from watching the students. He says nothing when she points out Jaune's transcripts don't match up with his performance in the field. When Jaune is appointed leader of team JNPR he's also the only person Ozpin congratulates. Possibly indicating he's actually impressed because he knows it was harder for the untrained teenager.
Now his interest to Glyndas' question might be partly to do with him considering Pyrrha for the Fall Maiden (*1) which means regardless of the actions of Jaune Arc he was watching the pair closely. If Ozpin is only interested in Pyrrha being a candidate then how she treats her partner is important. But the person she's paired with is still a big deal. This is someone Pyrrha would have to trust beyond the exam. I don't see him being fooled or letting someone she couldn't rely on be her partner.
This could potentially come off sinister depending on how much Ozpin knows and if he does why did he let Jaune go through with it? I've gone to a few message boards to see if this was discussed but it usually boils down to "Ozpin let him go through with it, Jaune passed thus Ozpin didn't care." That doesn't feel quite right to me. Would they really let anyone do this regardless of the rules? Keep in mind we already know of Ozpin making one big exception with Ruby who we know is important. Glynda didn't agree with Ozpin but didn't argue with him over Ruby going to school early.
Yet he cuts Glynda off much later when she noticed Ruby changed her story about hearing Cinder and doesn't say anything to the Pyrrha and Jaune partnership/the transcripts mentions. The first might have to do with Ironwood being in the room but my gut tells there are things Ozpin keeps from Glynda too. Things he knows she wouldn't approve of. No doubt she'd have something to say if she knew he intentionally let someone (Jaune Arc) in that he knew wasn't capable enough.
We learn from Weiss questioning the choice of making Ruby the leader that Peter Port trusts Ozpin to pick out the right people. The vibe I get from that is that Ozpin puts a lot of thought into that decision that the staff and him are fairly confident in who he picks. The staff rely on his judgement and he sees who works best in the position. It's important, more so than usual that year as there's a war on the horizon. Later on when he talks to Blake he mentions her not going to a combat academy and her being one of the few who didn't. I do wonder at this information, does that mean Jaune didn't have to fake his transcript? Does it mean that they would have to prove they could handle themselves some other way outside the actual exam? Regardless Ozpin claims that the entrance exam is all that really matters which is a possible clue that he did know the truth.
During the test Ozpin is very composed and barely answers any of Jaunes' questions. Jaune himself might have known about them fighting Grimm but he had no idea about them being tossed into the air. Since his aura wasn't unlocked at this point it means that if Pyrrha didn't save him then he would likely have died. The fact death is very possible is actually mentioned by the headmaster. Ozpin could have suspected that Jaune would be saved from another student but that's a big maybe. If he suspected Glynda wouldn't approve (and likely she would have made sure Jaune didn't take the test) why did Ozpin take the risk?
I don't agree with the idea of Ozpin deciding that regardless of faking their way in unprepared students would be allowed to risk their lives and only the results matter. While having a harsher side Ozpin does seem to value lives and I can't see him needlessly endangering regular teens. Which means he would have to have a reason for letting Jaune go through with it and ignoring Glynda when she notices something is off. There are two likely answers to this: Jaune having a high amount of aura and his family history.
We don't have much information on his aura at this point and it unclear how much Ozpin could know since Jaune had his aura locked prior to the test. Perhaps it's a family trait Ozpin knew about? What does this mean in the context of the story? How much is "a lot" of aura compared to the other characters? Does it mean Jaune will be powerful? The World of Remnant video on aura seemed to imply that there is another level that could be reached. To "become more than a man" like Ozpin. Would it matter if Jaune didn't have a useful Semblance? As far as we know there's no way to know what a Semblance is until it's brought out. While personalities do seem to relate to what Semblance someone gets Ozpin would have to really look into who Jaune is to know.
The Arc family legacy hasn't been mentioned too much we just know the previous generations were heroes, one was in a war and Jaune has their sword and shield. Despite Pyrrha and Weiss being famous in universe we haven't seen anyone remark on the Arcs. No one seems to expect more from him based on who his family is nor notice the shield/sword. The opening to volume one has Jaune staring up at the statues of warriors looking overwhelmed by expectations. The male warrior does have a sword that looks like the one Jaune carries and could be an ancestor. The openings have had hints to plot details like Ruby at her mother's grave so it's not unreasonable to think there's a connection.
So for now we'll assume those two factors plus Jaune having skills in leadership (which is discovered during the exam) are the reasons Ozpin takes an interest and decides to make an exception like he did with Ruby. How could he make sure Jaune didn't die? The only way I can see him having any power in this scenario is if he met Pyrrha and Jaune beforehand. We know he met Ruby before allowing her to come to Beacon maybe he did the same with them. He would probably see Pyrrha because of her reputation as a champion and we know he considered her the next Fall Maiden ever since he met her. If so he likely saw how isolated she was.
There are a lot of questions that come up with Jaune like why he didn't know about aura despite being raised by huntsmen or why he didn't know Pyrrha. But I could see Ozpin seeing those traits as things Pyrrha would latch onto. Her caring nature would make her look out for Jaune and the fact he treated her like a normal person would make him stick out. If that was the case it still seems like a big assumption since Jaune only met Pyrrha prior to the start of the exam because he was hitting on Weiss. He only hit on Weiss because he thought her sarcastic remark about him was sincere. Granted Jaune was bring friendly prior to this as he goes out of his way to help Ruby up. Jaune having taken his mothers' words about "strangers just being friends you haven't met" to heart. So he might have met Pyrrha by other means but that still feels like it would be leaving a lot up to fate.
The line up for the "send kids flying" could have been chosen by Ozpin. He might have arranged it so the students that are visible (not the shadowed versions) were the last ones to leave the locker room. Based on the fact we know Weiss left with Pyrrha, and Yang, Ruby and Jaune left together leaves me to think it'd be the latter if Ozpin really did plan this out. These characters are standing next to each other on the platforms and there are six people between Pyrrha and Jaune. If Ozpin knows then plotting for these two to get along in order to save Jaune is the only way he doesn't come off totally sinister. Remember this is the guy that calmly sipped his drink as Jaune was flipped into the air and even smiled. If he's not fairly certain of the outcome that is severely dark and messed up.
After this most of Ozpins' scenes relate to team RWBY and his inner circle. You could get some possible hints and double meanings from some of these exchanges that could relate to his reasoning. There hasn't been any real interactions with Jaune besides those in the vault that give any hints of how he views his student. It's noticeable that Ozpin does show concern when Jaune charges Cinder. Which is another reason I can't buy him being indifferent to a potential death during the exams. Ozpin was calculating there, he was amused and he made a point in his "wasted energy" speech that the rest was up to the students. In the vault he has little to no control on the situation, he's also worried about Pyrrha and Jaune. Hell I think it's the first time he calls Jaune by his first name (has he called any student by their first name?) indicating he has no time for formalities and trying to get his point across.
If Ozpin does have plans for Jaune I don't think he'd risk him in the vault or share this information with anyone. Qrow seems to be the most aware of his plots and knew of the importance of silver eyes. (Although Ozpin didn't apparently know Ruby had them until they met?) He wasn't impressed with JNPR outside Pyrrha (*2) but that doesn't tell us much. Qrow is more likely to know than Ironwood and it doesn't seem likely that Ozpin would tell Glynda after he refused to address it before. If he wasn't informed then Qrow will have to work little harder to figure out what is going on.
Right now the only idea that I can kind of link together is the possibility of the Beacon statue coming into play. If the male warrior is Jaune's ancestor then who is the woman? Given the hood I'm inclined to think it's a silver warrior. (Yes the man has a hood too but so does Jaune.) As far as we know Summer Rose went on her last mission alone. Maybe like in the past an Arc and SEW need to work together?
*1 Someone told me that when volume 1 was being made the Fall Maiden concept wasn't in any of the creators minds and came much later. If this is true the intention of the scene is that Ozpin IS interested in Jaune being mentioned not Pyrrha.
2* I found this weird since Qrow makes it sound like Pyrrha did all the work when that's not what happened. JNPR all pulled their weight on their team battle winning because of excellent teamwork, battle planning and strength. Sure Cinder set the match up but it would have been worthless if the team wasn't so together. While Ren got hit he still forced the sniper to chose a different target. Nora did all the powerhouse moves and Jaune's leadership made everything flow right. The only thing that went wrong was when Nora, Ren and Pyrrha stopped the battle to ask Jaune about his team attack names. In the end the other team looked worse for not doing anything.
Also I find it ironic that the same people Qrow insulted are the same ones that are sticking with Ruby.