The first thing that you need to realize is that it really isn't worth it. Some picks aren't great, but almost every champion has potential to be good with a player who knows what they're doing. Also, you can ask them to play something to improve your team comp. For example, you can ask your top laner to play a tank if you don't have have one and they want to play Riven or something. They can choose to listen to you, or not to. The big thing that you need to accept, though, is that it's not worth it to let your teammate's pick make you play worse just because you don't like it. You aren't them, you don't control them. Play as well as you can, no matter what they do, because it isn't worth letting their pick affect you like that. In the end, it's YOU who lost that game, not your teammate, because you didn't play as well. Sure, their pick is what caused you to tilt and not play as well, but in the end it's your fault you let it get to you like that.