Non-jewish Europeans had cultural mistrust of the Jews for centuries upon centuries, often resulting in ethnic cleansing and genocide in the form of pogroms. Hitler, and most of Europe, had grown up being taught to believe that Jews were horrible, inferior people, motivated by greed and all the negative Jewish stereotypes that persist today.
The judaic faith values education, and education ultimately produces success in industry. As such, versus non-Jews, the Jews during World War I had a seemingly disproportionate stake in business ownership. The Germans, with a long, prideful history of military might, having lost the war, immediately sought an excuse for the failure that resulted in their being stripped of a large percentage of their country's land, the forced implementation of economic policy that resulted in perpetual poverty, and eliminated part of their nation's identity: their military. So, the Jews, who because of their business gains were typically considerably better off than the typical German, were believed to be traitors who assisted the other side and stabbed Germany in the back.
Come to think of it, this sounds an awful lot like the Middle East with respect to the United States.
Regardless, Hitler rose to power promising a reclamation of the glory that was once Germany, capitalizing on the unifying hatred of the spiritually wounded German people. Hitler, a megalomaniac sociopath, who believed in the genetic superiority of a certain class of humans, took full advantage of the situation to further his personal agenda.
So in short, he killed so many people because he wanted to and he could. He hated Jews because everyone hated Jews, except he had a deeper hatred, possibly due to some of the other things that people had mentioned (like his mother or father's Jewishness, etc, stuff I haven't seen any undeniable proof concerning) AND he had the idea in his head that he was supposed to mold the world into a more divine image.
So in a really short assertion, I believe Hitler did what he did because he wanted to be or really impress God.
*edit*
And I'd like to add "stay in school", because I think it applies.