Should I stay?

I've been in a relationship for a while with a more than great guy. We have out ups and downs but lately they've been over the top. Whenever we argue, he immediately starts cussing and calling me names. He thinks whenever I'm upset or mad and I don't tell tell him why, it's his fault and that makes him super angry and defensive. He's never been physical abusive but the name calling and other stuff is really starting to get to me. I found out a little while ago that he has been talking to other girls on the Internet that are out of state and therefore "it's not cheating." He promised to stop but refused to apologize because he said it was my own fault because I've been hanging out with my "ex".

Ex as in a guy I dated for a year but we realized we were better off friends. We've been broken up for 2 years and I let him stay with me an year ago when he has homeless. We don't flirt or anything and he's in a long-term relationship with a girl who I am now best friends with that I completely respect. We're both able to make jokes about our relationship and give each other loads of advice on current relationships.

I'm seriously conflicted. He's such a sweetheart and a great guy on his good days, but other times he just finds ways to make me feel like shit. Any advice?