Black metal is just like death metal, but with satanic references and harsher vocals. Funeral Doom/ Doom is just like black metal but SLOOOOOWWWEERRR. Power metal on the other hand... well, let's just say that the world of power metal has never been the same since that BULLSHIT VIDEO GAME came out a few years back. Now, the sole purpose of power metal is to be the hardest song in that shitty video game, where people who are good at it think that they deserve the same credit as real guitarists. I don't hate power metal, I just don't like it as much as death metal. The "stoner metal" you refer to is actually a sub-genre of a sub-genre, thus it is not considered pure metal, but a derivative (much like how raw cane sugar is pure, and how MSG is it's derivative). With that said, you don't really hate death metal, you merely prefer it's derivations over it's pure form (this might be due to the fact that you were introduced to death metal too early, or your first death metal experience was with a shitty death metal band).
It's not possible for you to hate heavy metal. That would mean that you hate Iron Maiden, Judas Priest, and Black Sabbath. The "stoner metal" you refer to is actually a sub-genre of a sub-genre, thus it is not considered pure metal, but a derivative.
Oh, never say "I/everyone love/loves power metal" around death/black metal purists, that'll warrant an asskicking. Some dude in a Dragonforce shirt nearly got ripped to shreds at the AE concert. not sure if anyone actually harmed him, but he did get TONS of glares from the hardcore DM/BM fans.