Mulder's dad

IMHO, the reason Mulder clung to the fact that Krycek had killed his father was because he felt less about it than he should have. I think that Mulder's dad was abusive, mentally at least if not physically, and that his parents let him take the blame for Samantha's disappearance. They probably didn't say "Yes, Fox... it's all your fault!" But can you see them even talking about it? To a young kid, the silence on their part would have implied that he was at fault.

Mulder would therefore never have been close to his father... check out the surprise when his dad hugs him just before he's killed. When his dad was killed, he probably had little emotion- maybe even felt a little relieved that his father was dead.

He would have felt guilty for that. Beating up on Krycek was a way of trying to convince himself that he was a good son, that he did care that his father was dead.