First of all, I'd like to state that The Judge was an amazing movie, totally worth a watch. And to those of you out there who haven't watched it yet, I recommend that you do.
Now, as for your question, the movie depicts the estranged relationship of a father and son, who are -strictly saying- stuck with each other due to the circumstances. That is, Hank Palmer, a city lawyer hotshot, despite his hate and resent towards his father Joseph Palmer aka The Judge, wants to defend The Judge from the murder charges he is facing. The reason is simple. The Judge is his father. Period. Unconditional. He needs to do it. He knows he has to do it.
As for why the father harbors so much anger and resentment towards his son, Hank wasn't the ideal son when he was young. He was the kind of guy that everyone would have expected to be represented in court rather than to represent others. He drunk too much. He did not really follow his father's wishes as a teen. And finally, he got his brother in a car accident which ruined the brother's career in baseball once and for all. After all this, he left home. He got clean, started over, became the kind of man every father would be proud to call their son, but he never came home. His father never did get the chance to be proud of him. That I think is the main reason Joseph has so much anger towards him. In his mind, his son destroyed his brother's life, felt the guilt, started over, and never even bothered to look at the damage he's done.
But surely Hank also had his reasons, which I'm not going to go further into.
Joseph said that the victim of his murder when first presented in court reminded him of his son. The boy who was lost. The boy who can be fixed. So he gave him a second chance, which he went on to regret.
Again, this could've reflected poorly on Hank in Joseph's mind. As he may have come to the conclusion that like that kid, his son would never even really change.
This is my opinion on this, and truth to be said, a lot can be written on this subject as the movie is very deep in the message. I hope i was able to fill some of your doubts.