My ex girlfriend did something similar, so maybe my story can relate to you.
I knew I shouldn't have forgiven her, but she told me she didn't know what she was doing and that she really only wanted to be with me. Against my better judgement, I forgave her, and we continued dating. Things were never the same after that, though. It was always in the back of my head every day: "If she loves me as much as she says she does... why would she even do that? Why? Does she just not think of my feelings?" and it tormented me inside. At times she would notice this and she would get super upset and sad that she felt I wasn't over it. She accused me of not being able to trust her, and she was right, I couldn't. Things only went downhill from there and just a few months later our relationship was really on rocks and we rather violently (in a verbal sense) broke up.
Looking back on it now, I'm glad we're not together anymore. I could never be with someone who had such blatant disregard for my feelings and who apparently didn't love me enough to stay true to me.
You shouldn't be with him.
About a year later, I found an amazing girl and we've been together for over a year now. The amazing thing is that we haven't once ever gotten in a fight. I started realizing how my ex girlfriend used to get so jealous and upset at least once every two weeks, and looking back on it I see how emotionally abusive she was in our relationship. My current girlfriend is an angel comparatively and we have a brilliant relationship.