Am I unfaithful, or is it wrong to maintain friendships with guys I have dated in the past?

I have been dating a guy on and off for over a year. When things are good they are extremely fantastic, but when we argue and then break up it is almost always because he doesn't seem to trust me. I have a few guys that I met on internet sites that I am still friends with. I am not interested in them and don't have that much contact with them but they occasionally call me or comment on my Facebook page.
My BF goes bolistic and accuses me of having conversations on Facebook with them and that in a monogamous relationship I should not be talking to old flames. I tell him he is being jealous and that he doesn't trust me because I have told him over and over he is the guy I want to spend the rest of my life with. I feel like that if he trusted me he would let it go and believe that he is th only guy I am interested in. I feel like he is trying to control who I am and am not friends with.
I never initiate the exchange, it is always the guys who leave me a comment or text me.
Should I break off all communicatiom with these guys as my BF wants or does he need to trust in my love for him and trust me when I say there is nothing there with these other guys. BTW we are both divorced after over 30 years of marriage, so we are not young people.