Questions: Break Up & Divorce

I broke up with my boyfriend. He isn't taking it seriously. Because, when we argue sometimes I block him. But, I actually do want to move on with my life without him. I feel kind of guilty for blocking him because I think it feels cruel. But, I don't want him saying sweet nothings to me to where I FEEL like working things out.
We have fundamental disagreements. He had inappropriate online relationships when several different women. He has stopped the inappropriate conversations, but he still talks to them from time to time. Even though they are regular conversations NOW, it doesn't change the fact the he is still in contact with these people.

Sad to say, but the question was inspired by my parents.

My mom was and still is miserable being with my father and talked about leaving him a lot growing up, but never did. She has become extremely bitter, even now, that she didn't do more with her life because of his expectations of the women in the family and now his medical issues forcing her to care for him even further.