I don't ship H/D because I think that Harry and Draco could ever "fall in love". I've been in love, I've been both on both sides of the "unrequited love" coin and honestly? Love as defined by mainstream society, the idea of unconditional caring for another person, is fucking overrated, not to mention a pipe dream unless there are conditions placed on the word "unconditional". The very idea of "unconditional love" makes me twitch because what do you mean unconditional? Human beings are not dogs to give their loyalty and trust unconditionally – hell, even with dogs, you've got to treat them well to earn their trust and loyalty when they're puppies.
The only thing in which dogs differ from humans in this is that if you've got a dog's loyalty, you'll have to kill it before it stops trusting you. People aren't like that, though. Not only does most adults' trust have to be earned, but it's very easily lost – people can lose trust on the basis of mere accusation; even the most loyal of us will hesitate and waver when the trustworthiness of someone we care about/trust is drawn into question. We're not unconditional creatures by nature – we're capable of unconditional feelings but it's not the default modus operandi of a human to do things and get nothing in return. We'd have died out long ago if it was.
Back to love, though.
The kind of love that everybody dreams about, the kind that lasts forever, no matter the weather? Yeah, it exists. I'm talking about the kind of love that endures even beyond death – the kind of love where you know that the other person isn't flawless but you love them anyway. It's funny, because the way I was raised, that's the kind of love I feel for my parents, my family. That's sort of … almost obligatory, though, part of my upbringing was that family comes first no matter what, and perhaps that's another reason why I identify strongly with the Slytherins in HP, because on one level, they're all about family, and I get that.
This is why Draco is capable of love, too. I get that a lot of people would simply like to think of the Malfoys in the way JKR intends them to come across (and loudly says so) – posh family who spoil their child rotten and take no responsibility for his appalling personality. Whether or not she intends this or not, the Slytherin idea of "family first" is a form of "unconditional"* love that's admittedly entirely arbitrary, but nonetheless it's love. I'm not a fan of my father as a person, but I'll fucking kill anyone who tries to harm him. I may gripe about my grandmother being a nasty old wench with a bad attitude, but I'll still cook her dinner and clean the flat and do the shopping, because I want to take care of her.
It's different with non-family members, obviously. The desire to take care of and support family members may arise out of a sense of obligation, I'll not argue that. However, once you're faced with people who are outside of the family circle, you're dealing with the issue I brought up above of having to earn trust and loyalty – once that's there, when can you say it's unconditional? You can't, really, but there usually comes a point where you know that there are certain people in your life, friends of yours, for whom you'd do anything, who are "like family" (ahaha, you knew this was coming, surely?). The way I see it, this is where love begins – with trust, with loyalty.
So when I think about H/D, I'm not worried about their personalities as much. Yeah, Draco's a bigoted bully. A bigoted bully who loves his father enough to threaten revenge to Harry Potter, a boy who's powerful enough to not get killed by the most powerful wizard in existence, four times. Yeah, Harry doesn't give a shit about Draco because Draco's a bigoted bully and Harry knows that all Slytherins are stinky and mean anyway. Harry's prejudice is more toxic to the ship of H/D than Draco's and so it's Harry who needs to be shown that like every other person, Draco has other layers, too (not in canon, he doesn't, obviously, because canon's told from Harry's POV and Harry doesn't see anything but the two-dimensional bully).
Both of them, however, have the human capability for trust and loyalty and both of them as individuals have the capability to reconsider, to change their mind. To me, Harry/Draco is all about changing your mind and seeing the good in someone whom you believe to be a bad person – never possible without specific circumstances; stuff has to happen for these two boys to even consider that they may be wrong about the other. It can be something as inconsequential as Harry seeing Draco cry at his mother's funeral or Draco overhearing Harry say something that goes directly against Draco's perception of Harry. The point is that this ship always works once they're put into circumstances that force them to re-examine their views on one another.
Forget clichéd scenarios for a second, what makes this a unique thing between Harry and Draco? Don't all other characters have this potential, after all, to see another person they formerly believed to be bad in a new light? Well yes, they all do have this potential. What makes H/D special for me, and viable as a ship, is that Draco and Harry can be both made to respect the other, based on their canon characterisation alone. Respect is the first building block of trust, after all, and it doesn't require a great leap of logic to imagine Harry having respect for Draco if Draco deserved it – Harry's fair like that, bless him. As for Draco, it also doesn't take a great leap of logic to see him respect Harry – half-blood or not, the things Harry does are impressive, he's a powerful wizard, and Draco can respect that, if nothing else. He may be jealous and resentful and he may whinge about it, but at the end of the day I still think he can respect Harry for what he does. From there it's not a long road to respecting Harry for who he is.
You'll note that I haven't mentioned sex at all, and there's a good reason why I didn't. I don't think that sex consummates a relationship. Sex often begins it, actually – and when I say "sex", I mean physical touching of a sexual nature of any kind, not necessarily penetration. There are lots of ways to have sex, but sex in a romantic relationship that's between two people who love each other is just the icing, and in my experience, sex is quite unnecessary for love to exist. The person I love the most (not a relative) has been dead for over 10 years, and I'd never had (or wanted to have) sex with him while he was alive, either.
For me, Harry/Draco is not about the sex at all. I don't complain that it's there and I write it myself, natch. But the point of the ship, to me, is giving one or both characters the chance to see the other as a human, rather than as a cardboard cutout villain because you can bet that to Draco, Harry's as much a villain as Draco is to Harry. The way both characters are portrayed in canon, there are plenty of characterisation-based opportunities for them to understand each other, to learn to trust each other and to become the sort of friends who are like family. The romantic swoony feelings that make people giddy and the sex are really incidental. While it will never happen in canon, I believe that Harry and Draco as characters have the potential to form a bond that would outlast the death of either one and make both stronger while they were living. I believe they can be friends.
And that's why I ship Harry/Draco.
* Aside from the whole "they are family and if I support them, they'll support me too" element. I'm on the fence in the "altruism in human evolution" debate.