Why is he filled with hate? Oh, you know, only because he was framed for the murder of his Emperor, which resulted in Asura's numerous deaths, the murder of his wife, and the imprisonment of his daughter.
How do we know Asura is filled with complete and utter hatred? Because his game has "wrath" in the title, and all four hours of it involve him screaming really loud and punching things so hard that the entire planet of Gaea feels the ripples from his swings. And boy, does the action tend to escalate quickly. Take, for instance, the time Asura shares a nice, hot bath with his mentor-turned-enemy before beating him senseless. Asura didn't win all his battles, though--not at first anyway. He died and was "reborn" plenty of times (remember when he got karate chopped in half?), with his rage growing even more powerful after each resurection. Harnessing the power of his hatred, he was finally able to overcome all odds and save his daughter Mitra from the clutches of evil.