Harry had also come to realize that Tom Riddle was never going to quit until Harry killed him, or was dead himself. Not because of a stupid prophesy made by a drunken mush-brain Divination teacher, but because Riddle was a psychopathic terrorist, and you can't reason with insane people.
He made himself a 'what to do' list, based on what he was able to conclude so far. Ignoring for the moment that this was most un-Harry-like behavior, he surveyed his work:
Fact: Dumbl can't be trusted. Action: Action: avoid and ignore.
Fact: I am emancipated and rich. Action: be my own man.
Fact: I have 3 libraries. Action: read them.
Fact: I'm tired of being the victim. Action: take charge of my life.
Fact: People around me are sheep. Action: give them a new shepherd.
Fact: Dobby's English is weak. Action: Help him with it.
Fact: I don't know much magic. Action: learn more from my 3 libraries.
Fact: Voldemort's a dick. Action: Kill him.