Dumbledore actually lied again. Harry and Voldemort basically get stuck in limbo, where he has some kind of magical conversation with Dumbledore (I’m not sure this is ever explained). Voldemort’s Killing Curse once again failed to kill Harry, and instead destroyed the portion of Voldemort’s soul latched onto Harry (again I don’t think a Killing Curse was originally able to destroy a Horcrux and this is also never really explained). Basically, just as Voldemort was unable to die while Harry lived, so too Harry cannot die while Voldemort lived. But now the last ties between them have been destroyed.

In order to destroy a horcrux, it has to be obliterated in such a way that it could never be brought back. If the horcrux is a living thing, you can just kill it by any method because magic can't bring the dead back to life. So if Voldemort had killed Harry, he would have destroyed the unintentional horcrux he created.

I think technically speaking he did kill Harry, but the remnant of Lily's protection saved him from dying all the way, and that's what caused him to meet Dumbledore in limbo or wherever.

I think it's fair to say that this plot point was kind of contrived and not really set up in universe, and although the specific magic that allowed it wasn't set up, it was a recurring plot point throughout the entire series that Harry never asked to be the chosen one and didn't like it, so the moment with Dumbledore represented him being "reborn" as a hero by choice rather than by random chance.

Honestly I don't get why every leftist wants me to hate the Harry Potter books. JK Rowling may be a piece of shit, but that has literally nothing to do with the content of the books. It doesn't matter if you're the most despicable Nazi ever to Hitler, if you write a book that captures the imagination of millions of kids and doesn't contain your ideology in it, you've written a good book. Hating everything associated with someone doesn't mean you hate them more.

edit: ok, I don't mean the book has to "not contain your ideology," that's impossible. What I mean is it has to not serve as a vehicle for your ideology, and it has to not contain so many problematic themes as to set it apart from other media in the same cultural context, which I believe applies to the HP series. I acknowledge the serious flaws in the books, but I think they should be looked at completely ignoring Rowling's stated political views, which people clearly are not doing.