Doom metal is not a genre, it's an aesthetic qualifier for slow stuff. There's no way one can seriously put Sleep, Esoteric, Cianide, Winter, Witchfinder General, and Thergothon (all great bands, by the way) into the same genre of music.
Even '80s doom, like Trouble, Candlemass, Witchfinder General, and Pentragram, shows some wild variation. Most modern stoner doom is pretty lame, but Electric Wizard and Sleep did some good shit in their heyday (Dopesmoker and Holy Mountain, respectively.) Death/doom like Cianide, Asphyx, Vallenfyre... that stuff is nowhere near a cohesive genre either. Stuff like Eternal Darkness is pretty much death metal's take on Candlemass and Solitude Aeturnus, Asphyx and Acrostichon are barely doom meta at all (more like slower death metal riffs sandwiched between fast tremolo stuff), Winter is almost more of an outgrowth of Axegrinder-style atmospheric crust punk than it is metal, and then there's bands like Cianide, who take multiple generations of "doom metal" and synthesize pentatonic Black Sabbath stuff with Hellhammer and slowed-down Master riffs (check out the first few minutes of "Gates of Slumber" for a great example of this). Some of the better modern doom metal like Hooded Menace and Decrepitaph build off of that style. There's also sort of a doomy out-growth of "melodic" death metal (which is kind of a fake genre in its own right, but I'm not touching that clusterfuck) with stuff like Misanthrope, Katatonia, and Cenotaph.
Funeral doom, however, really is something of its own sub-sub-genre. It takes the high/low guitar dichotomy of early Emperor to a new level of complex orchestration: think of the layered riffing on diSEMBOWELMENT or Thergothon's full-lengths. When you hear a funeral doom riff, you know it's different. In fact, funeral doom bands and "regular" doom bands ran into quite a bit of conflict back in the day, as a cursory examination of the thank you lists in the liner notes of Electric Wizard's and Estoeric's early album attests.
Basically, I don't really get how someone can hate doom metal, since doom metal is literally just metal played a bit slower. It's like hating anything painted blue or in the key of C sharp minor. You could even make a case for calling Burzum or Incantation doom metal: are they any less doom than Asphyx? Doom metal isn't a real genre; it's mostly just a useful term for identifying certain characteristics in music.