My father says its not fair to cut him out of my life...?

Thats a hard one. I wouldnt suggest cutting ties with your dad. Life is too short to hold resentment over petty things, you dont have to have a relationship with his wife though. When you call only speak to your dad or half sisters, dont even deal with her. My dad remarried a woman that I cannot stand either and I chose not to have a relationship with her after she said my sisters daughter was the first "girl grandchild" and my daughter was 3 yrs old at the time. Because she knows I dislike her she no longer even tries to speak to me and it works out fine for the both of us. If my dad so chooses to stop contact with me because of my relationship with his wife, thats his choice. I tried to keep a relationship to the people I am related to.