The accords mean absolutely nothing

Thunderbolt wasn't wrong telling Tony he's lucky to not be in one of those cells after the airport fight. To me, this is Tony cracking down trying to use logic and reason, but he's too emotional a creature. He's egotistical, which means he thinks every position that he takes is that much stronger for him taking it. Because, like a lot of people with big egos, he considers his intelligence as a source, and would probably truly cite himself in an argument.

I think that he had some moments where he was trying to reign it in because he does have an obligatory sense of doing what's right for people, but again, it's ego driven because he thinks people are small and they he owes it to them to protect them. I know he feels emotions and pain, but that woman at the elevator in Civil War, she's an ant to him. It's important, maybe more important, for Iron Man to act on her behalf because it sets the example for what's right, not because he's consumed by emotion. When he's really consumed by emotion, like you said, he does what he wants. Funny enough, when he's consumed by those emotions is probably when he's closer to being right. Captain America said it during their debate; the accord could send them where they're not needed or stop them from being sent where they are needed. It's legalese and paperwork, but once there's a chance to get on that ship with Strange, he doesn't sit and wait for permission. He'll just do it, and probably never let you get a word in unless you're even more egotistical than him. No easy feat but Strange has his moments.

In Iron Man 2 he was certain that it was his right as a private citizen that the government not confiscate his technology. He sometimes tries too hard to lead by example from the pedestal he thinks he needs to be on to honor his deceased parents. Accords Iron Man would try and arrest Bucky and make him stand trial for murdering his parents, but real Tony doesn't care because "he killed my mom".

I could be reaching but that's why Rogers is so fed up with Iron Man, even though he cares for his well being. He's fed up because he knows that even when Iron Man is right, it's usually for appearances sake in front of Ross or other government persons. Rogers sees through it because Tony's making the arguments he makes because he feels he has to, not because he wants to. That must be frustrating, but for some people, being right is more important than being reasonable and that's Tony.