Cotton was a terrible father, but he had his moments with Hank

There's no other way to put it. Cotton was a horrible HORRIBLE father. But in instances like S3 E5 when Hank needed to hear the truth from a father figure? Cotton provided. Granted, he's still a piece of shit of a dad, but he really does have his moments. "If it's a contest on who's the better daddy, you win! I mean you made Bobby! All I made was you!" Very shitty but very well needed to be heard by Hank. When Hank says "What if I keep trying and it doesn't happen" "Well then you had the fun of trying, boy!"

Cotton did care about Hank. He was a shitty father, hated the fact Hank was his son, because he regretted having a child with Tilly (hence why GH was the favorite. It wasn't a child with Tilly. Or with Junichiro, Tilly wasn't the mother). But in the end of things, Cotton really did have at least a LITTLE love for Hank. Unfortunately, his hate for Tilly overwhelmed that, but it was still there. Cotton loves his children. He just hates that he had one with Tilly, and unfortunately that's Hank.