Hey mickey, I can say from my own experience, this is a form of control on their part over you. It is also a lack of self confidence in themselves. My ex was that way. Unless they get professional help, this will continue to happen to you. There is nothing you can do to prove them wrong. They will always feel you are cheating on them. They will always threaten to cheat on you, and some day they will.
This is not a healthy relationship. I have seen talked to others in the same position. Even though you love the person, your well being is more important than a relationship that ends in mental abuse.
My thoughts are to get help for yourself first. Don't allow his excuses run your life like he wants it to be.
Keep in touch. I hope others will have other insights.