The guy I like is mad at me over this stupid conversation. Should I apologize?

I don't think you should apologize to him unless you really feel bad about what you said, and you regret it, in which case you should apologize. However, if you feel he was in the wrong then wait for him to apologize. In my opinion, there were wrongs from both sides, so I would say that an apology is warranted from both people, and then put it in the past, and move on.