Before he became Voldemort – he was Tom, and although he has tried to eliminate all traces of the boy he used to be. he cannot eliminate his own mind. Although sometimes he thinks wiping ít clean would be the preferable option. He hasn´t forgotten what Dumbledore told him, that his neverending quest for knowledge and thirst for power are distrubing and that he should not quest for immortality. But how can he not when death is such a cruel master, something to fear and abhor? For what would wait for him on the other side – but nothingness?
Death has torn his mother away from him, taken her before he had a chance to give her a reason to live. His sire has never shown any interest in him, so he won´t wait in the afterlive for him either one day. And hasn´t Dumbledore himself lost his beloved sister to death? So how can he not hate it and try to find a way to conquer it? How can he stand there and deprive him of the only real home he ever knew, saying he isnt´t fit for the position. He is good at Defense against the Dark Arts, he knows them inside and out. He knows it is about the intent that makes a spell evil, for can´t you kill someone just as easily through a well thrown “Wingardium Leviosa”, Stupor, Taglarantella or Bombarda? All Spells that have been declared “light” - Dumbledore is wrong about that – and if he is wrong about this, who is to say that he isn´t wrong about other things as well.
He needs to learn more, so that one day he can show the old man that he is right. Then maybe he can come home, home to Hogwarts. So he continues on his quest to gather more knowledge - Hogwarts always on his mind.