My ex boyfriend claims to love me yet thinks so differently than I do.?

We started dating about 1.5 yrs ago, broke up about 6 months ago and have been off and on trying to work it out. The problems started when he cheated on me when I had gone out of town to visit my mother. We had been fighting all that week but I called and informed him of my departure and probable return on a vm because he didn't answer, I spoke to him the night of my arrival to my Moms, we were still at odds and he kept asking me where I was, suspicious of my where abouts, I ended up getting angry and telling him I was in Las Vegas and hanging up. When I returned my best friend (who's boyfriend was my boyfriends pal) told me Jamen had spent the weekend and a girls house. I immediately called him and he tried to deny, I screamed at him and hung up. The next day while I was at work he text me thad he had a 3 way with another man and this girl because he thought we were broke up because of the fighting before my exit and my statement about Vegas. Nothing was ever said about breaking up, he swears in his heart we were broke up. Yes I know, WHATEVER. Stupid me took him back never believing his ridiculous story and telling him so. I tried to forgive but would often have spurts of anger and say vicious things to him, he would lash back still saying it wasn't his fault because he thought we were broke up. OMG, why I stayed I dint know. I don't know why I keep trying to continue this relationship. We fight and it always comes back to his cheating and him saying he thought we were broke up! How can I explain to this low IQ his excuse is lame?