One of the myths often spread about Jason is that he's arrogant. In fact Winick himself has used to this idea in UTRH, it's one of the descriptions given to Pre-Red Hood Jason. It's not really accurate. There have been retcons after his death to make him look bad. (*1) None of the ones I read ever gave me the impression that he's more arrogant than anyone else in the family.
Members of the bat family can come off arrogant but I wouldn't rank Jason near the top. Bruce, Damian, Barbara and at times Tim. (Especially in Red Robin by Fabian N. ) With those members their either a little full of themselves and/or their skilled enough that they sometimes underestimate situations. I don't believe Jason is arrogant like some claim simply because I don't think he's nearly as confident as these bats are. He knows he can beat the crap out of certain people sure, there's just not any ego at play. Many of the things he says are part of the tough guy façade. Sure there can also be some insecurity to play with those I named but in a lot of cases they really do think their in the right unless proven otherwise. Like Barbara believing she knows better than Nightwing on who he should date because she's smarter than him. (*2)
And no I'm not try to put down Bruce, Damian, Barabara and Tim. It's a character flaw, every character has their own flaws. So bear with me if this doesn't come out right as it's hard to explain. There are times when these four are oh-so-certain of something whether or not their actually right. Bruce knowing there were no Court of Owls. Damian knowing he can take on any foe, etc. With Jason there isn't that sense of certainty in himself. Which does make sense since he grew up in an uncertain place with few people ever believing in him. Some actually blamed him for his own death so naturally he's not going to be very prideful and/or see others as his inferiors. Why would he when so many have treated him as an inferior to the point he buys into it? Jason doesn't see himself as anything special just another Robin not a son. He's shocked that Isabel would have a serious interest in him. The guy believes she's better off without him and thinks she's nearsighted for liking him.
In Lobdells' two origins Jason either thinks he's too much of a bother for Alfred/Bruce or that he shouldn't be Robin. Jason isn't used to the limelight or getting positive attention. Dick might like the spotlight but Jason isn't as comfortable. (*3) He's shocked that people cheer for him and awkward when someone personally praises him. Perhaps he heard positive things when he was working as Batmans' partner from those he saved. That's less personal than it is when he's Red Hood because part of him has to think their cheering for the Robin legacy, not him.
So far the attention he gets--at least from the ads--seems to be directed at his connection to the bat family. Jason isn't aware of Roys' conversation with Battleworth at the start of RHA when she thought he was the boss and wouldn't bother with Roy without him. He might have overheard one of Battleworths' men commenting on it being odd to see Arsenal without Red Hood and thought nothing of it. For good reason too as Jason is used to people underestimating him which he takes advantage of when he can. Out of all the bat kids he's the one that gets the least amount of positive feedback. (*4)
Of all his supposedly arrogant moments I can trace most back to Jason acting more confident than he feels, frustration or banter when dealing with bad guys. Lobdell has had Jason shrugging off understanding what Bruce was showing while silently admitting science was the hardest thing to learn. That he's really trying to impress Bruce and prove himself to him. Jason does come off almost like Damian does in terms of pride from his early days with the All Caste and his attempt to take over a mob at a funeral.
I think too many write off Jason because of what others say and don't see why he acts the way he does. Stories like Hush mention him and reduce him acting like he did nothing to earn his role as Robin. He wasn't perfect but then again none of the Robins are. Many made the same mistakes and worse yet those missteps are forgiven and soon forgotten. Out of the current main bat family I'd argue that he's the most humble. Dick might not have act arrogant as much as the ones I listed (at least in most stories) but he's still a performer at heart. He's used to the attention and kind words. Jason isn't and most of the time has trouble believing it when he gets it.
I'm not saying Jason can't be arrogant, if anything I think he was during the time between his All Caste training and returning to Gotham. But I don't think being arrogant is one of his main traits like everyone seems to think. Does any of this make sense?
*1 DC tried to sell the idea what it was Jasons' fault for getting killed but really nothing they wrote convinced me of that. Not just because I read the original street kid Jason Todd material. Even when trying to make him the bad kid DC still made him more relatable than the distant and cold version of Batman they wrote.
*2 This was in Graysons' Futures End issue where it's implied she said this before he became a spy. But she's also acted like this under Seeley in Batman Eternal.
*3 Jason is visibly uncomfortable when he's asked to say a speech in front of the All Caste. All he can manage is an awkward thanks. Later on in the same issue (RHATO #5) Roy comments on Jason being an awkward public speaker.
*4 Even Dick said Jason still hasn't proven himself in Batman and Robin after Damian challenges them all. Only Alfred and Tim haven't been negative towards him (although Tim did think poorly towards Jason in the TT DOTF tie in.)