It's because if Jin did not forgive him, in the end Jin is no better than his Dad. But since Jin is more human than his Dad (thanks to his gf who's made him more human) he's forgive him. After all despite his Dad is psychopath, he still he's father.
Well it's my opinion tho.
Not killing his father was right I admit that what I mean is that his choice of words was bad cause when he said he forgave him it felt like he forgave him for killing Manny & manny's family & selling those innocent poor girls organs after killing them without a reason & etc.
He became the better person, the bigger person, completely opposite to his dad by forgiving him. It was the right thing to do. Probably the best.
Seriously how could jin forgive him? Not killing him was okay since he would go to jail in the end anyway but forgiving him? Ugh it just bothered me so much , like instead of forgiving him he could say "you don't even worth killing " or " I don't want to dirty my hand with your shitty blood" or something like that