Can I fix this trust issue?

Hello everyone I am in really tricky situation and I am just looking for answers on how to solve this. My boyfriend has serious trust issues with me and at this point I am not sure if I should keep putting in work to get him to trust me again. He always brings up two main examples of why he doesnt trust me which is in the early stages before we started dating I went on a trip and saw a guy that I was talking to before. We kissed but after I came back I decided I wasn't interested in that guy and decided to get more serious about my boyfriend. But a year later he found out about the whole incident and says that it looks suspicious I never told him. The second situation was two years into the relationship we broke up. During that time I kissed one guy but we got back together a few months after the incident. He claims that as soon as I kissed the guy I should of told him but my point to my BF was at the time we were not together so why would I feel obligated to tell you. But he uses that to say I was hiding something and I am a snake. I really love my boyfriend and I want this to work but I feel that everything to him is an issue. He even said that I put my situations where a gives me attention and flirts with me and he believes there are girls out there that can avoid a guy flirting with them. Now because he has trust issues with me if I even cry out to him that he is treating me cold he resorts to saying I am cheating on him or met someone else. We both agreed that we will try to work on the trust issue but then he will say things like it should be easy to gain my trust and I am not sure why you can't do it. And Is this normal for a guy to behave like this.....do I deserve the way he is treating me because of those two incidents. Please help me figure out if I should continue working on getting him to trust me.

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