honestly dudes, i never fully understood why jason wanted revenge on bruce until i really analyzed the situation. So here are my thoughts (which nobody asked for):
Jason grew up in the bad part of town- the part where you don’t call the police for your problems, you solve them yourself. Bruce’s vigilante justice is the same thing, so jason grows up believing justice and revenge are one in the same.
The fact the Bruce let the Joker live means that the crime (jason’s murder) is still unpaid for. So Jason will serve justice himself- he’ll kill the Joker- and then, he can finally make his peace. But Bruce disagrees. Bruce thinks the punishment has fit the crime, and Jason interprets this as Bruce not caring enough to take an eye for an eye.
So Jason tells himself, if i cannot make Bruce sorry I died, I’ll make him sorry I came back.