Is it normal to fight and not want to be alone

go chuck Norris.

Is there a difference in who pays rent? or do you earn more? If he asks if he should leave then I'm guessing there is.
For a guy, this could be on his mind on some level (i was in a similar situation). It can be emasculating at times. Try to speak with him and reassure him
that it is a balanced living space and just as much his as it is yours. (or come to an agreement between yourselves that you are happy with in that respect.)
I also agree with Anime7, tell him how you want to develop a better conflict resolution.

Some people just wants to get out of the heat because their scared they might say something they'll regret.

this is so normal.. i also want the same but my boyfriend ask me for some space after every huge fight. but nowadays he getting better..!!

That's very mature of you. I think you should tell your boyfriend this so maybe next time when you fight it'll turn out differently. Good luck.