I thought I could forgive him but I'm having trouble

My boyfriend and I have been dating for about 2 and a half years now. About 8 months into our relationship he cheated on me, having sex with a girl just one time. On top of that he did it while I was sick with the flu (literally vomiting and having diarhhea simultaneously all night) and he then introduced her to his boss, then they started dating, and we hung out with the girl and his boss all summer. He made me become friends with her after he cheated on me with her. He told me almost a year after it had happened. And I decided to forgive him. He has apologized many many times. Since then we have moved in together. The only issue is that I thought I could forgive him and move past it but I still think about it every day.. Even though he told me like 8 months ago. I still think about breaking up with him, still question how he could do such a horrible thing. For years he has had issues with lying but is trying to work on it and I think I see that. Since he told me about the cheating he has admitted to a lot of lies as well. I just can't help but think that I deserve someone who hasn't lied to me or betrayed me, because I have never lied or done anything to betray him. When I feel sad about it and I express it to him he says that he hates being reminded and gets irritated.