Why couldn't Lord Voldemort kill Harry Potter?

It's a very complex matter, I'm afraid. When Harry's mother, Lily, died to protect him, she left behind a very old piece of magic. This magic meant that as long as Harry could call Lily's sister, Petunia's, house a home, then Lily's protection would run through his veins and Voldemort would not be able to touch him.

When Voldemort took Harry's blood in Goblet of Fire to regenerate himself, he did not know that he was also leaving behind a part of his power inside Harry, too, that made him untouchable.

Although we do not discover this until the final book, a part of Voldemort's soul attached itself to Harry on the night that Voldemort killed his parents. This is the true reason that Voldemort was never able to kill Harry - he would have been killing a part of himself.