Actually insane about this
In his mini comic, Roy doesn't want to be like Oliver and doesn't have aspirations to be the next Green Arrow either. But he still wanted to be worthy of it, he wanted to be considered and acknowledged. He wanted to be his own man, equal to GA. He needed Ollie to look at him and say he trusts him, sees him and respects him. To acknowledge Roy is making an effort to be a better man. We, as readers, know Roy wasn't ready yet, maybe Ollie knew it too. Hell maybe Roy knew it as well, but to know something in theory doesn't mean you can't be disappointed and hurt. Here he got a clear message: Oliver didn't consider him worthy.
In JLA '06 Roy is finally his equal, he's Red Arrow and he's in JLA amongst gods and people he looked up to his whole life, he's been in superhero business longer than some of them and he knows it. He doesn't question why he's been invited and not Ollie, because he knows he's worthy of it.
he answers a question about his physical wellbeing, but he doesn't say "I'm good", he says "I'm perfect". And he knows it. He's confident and doesn't doubt his abilities or his position in the league. He called himself Red Arrow because he's an equal to Green Arrow. It's a family business and he's no longer being left behind.