He broke up with me, but doesn't want me to go. Why?

My boyfriend and I are having a couple rough months. Fights tend to get bigger as we go along. Our relationship is quite difficult. I'm a talker, that's how I fix things. He's a shut out type of person, doesn't wanna talk about it. It frustrates me when we have an issue and I wanna talk about it and he just ignores me to my face. I won't lie, it pisses me off and makes me angry. So we fight.

Anyways, he tends to go to the bar a couple nights after work. One night. I woke up, it was late, and he wasn't home. I called him, some girl at the bar is buying him drinks and that's why he hasn't come home yet. Of course, jealousy filled my head. I tried to talk things out with him and I asked if he could stop going to the bar until we can fix us a little bit. I felt like the bar was just making things worse. He agreed. But then the next time he wanted to go to the bar. I didn't even get mad all I said was I thought we agreed to work on us some more before you started to go back. He said okay. And then ignored me for days afterwards. Three days go by, (btw we live together) I finally ask him what's going on why is he being distant with me. And he ignores me and we fight. He breaks up with me. It's been a few days now since he broke it off. When I try to talk to him, he says it's still over. But he asks to sleep in bed with me. If I mention about finding a place of my own and moving out, he acts like I'm the one leaving him. I've tried talking to him, tried fixing it. But he's still set on breaking up. He's full of compliments now and cuddles. I'm confused. He doesn't help. Like today I asked him if this is for sure what he wants to do. He said yes. And then started biting his lip and looked like he was about to cry. I asked him what's going on why was he biting his lip. He just laughs and made up some excuse of why.

Are we breaking up? Or is this just a big head game?
He broke up with me, but doesn't want me to go. Why?
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