Why did Harry choose the horcruxes ?

I have often wondered what if Harry had decided to give up on the search for horcruxes and instead had engaged in the quest for the hallows.


Did he do it because he was supposed to do it out of some responsibility ?
Did he do it because that was the right thing to do ?
Did he really have a choice ?


~nightflier


P.S. In my head all those questions have an affirmative answer. I guess 100 points to gryffindor then :D