When my boyfriend and I get in an argument he always says things about my family, things he shouldn't say. And when he's cooled off he says he said them things about my family to only get me mad, what should I do?

You should explain to him that it's not okay for him to say those things and then try to redeem himself at a later time. Make him aware that you don't appreciate his comments and games, and that you won't tolerate them. Then stand by your word. If cares about your feelings, then he will respect your request.

Well put. If he keeps going on about your family in fights, after you telling him not to, then there needs to be consequences.

You should break up with him? A guy that control his emotions and stupidly insults his girlfriend's family? Why would you want ANYONE that is like that around you? Make him respect your family or send him packing. And afterwards not only does he not say that he is sorry but he tries to excuse himself? Come on...

Good luck,
Javi

Is he old enough to know better? If so, I would break it off. He is immature still and not ready to be in a healthy relationship.
He has already shown you a pattern of behavior.

Talk to him about it if you want to and see what he says about it. Then think carefully about his answer. You will either learn that it is likely to keep being repeated, or that he may really want to change the behavior.

I am assuming this has happened more than once. He does it, you accept it.
Tell him it hurts and don't do it again. If he does, leave him.

The first thing smart couples do is set the rules for disagreements.