I was growing up and getting into comics when Tim Drake was Robin, so the first thing I knew about Jason Todd was that nobody liked him. That definitely colored my opinion before I ever even read a Jason Todd story. I went along with the consensus, immediately taking the character to be a grumpy, insolent jerk who just didn’t get how awesome it was to be in the very presence of Batman.
I stopped reading comics almost completely when I was teenager (in fact, I stopped reading superhero comics altogether, and instead went through a manga phase). When I returned to the genre, I brushed up on some Jason Todd stories and became acquainted with what had happened since I’d stopped reading. Gradually, I started realizing that, while it was cool to hate Jason when I was younger, he’s actually a very complex character. His anger toward the world and toward Batman is justified, and he asks the question that I think every Batman fan has wondered about: why doesn’t Bruce just bite the bullet/take one for the team and kill the Joker? We may or may not agree with Jason’s feelings of betrayal at Bruce’s refusal to avenge him so fully, but I think it’s completely understandable for Jason to feel that way. And while Jason rejects Bruce’s nonfatal methods, he is essentially fighting the same war.
Jason getting involved with my favorite character made me pay even more attention to him, at which point I realized that I’d become a fan of him.