Hmmm...my personal reasons? There are so many! Well, in no particular order, here's what I've got:
1) Hermione was rather quick to get off the topic of Harry kissing Cho. She was speaking "briskly", as if wanting to end the conversation. It was clear she wasn't comfortable.
2) Since when has Ginny taken Hermione's place in the Trio? Smart, pretty, funny, fun - who does that sound like to you?
3) Hermione always has Harry's back. She taught him the Summoning Charm when he was desperate, even staying up all night to help. She was the one who went back in time with Harry - not Ron. She stood by him when Rita Skeeter slandered their names, and helped him stay strong. She was determined to go with him when they rescued the Stone. There is more, of course, but that would take up gigabytes of space.

But the point is, Ginny's never been there for Harry. She's been too busy "playing the field" to provide support of any kind.
4) I know this one's been said all over this topic, but Harry/Ginny was short, undeveloped, and rather cold. All they did was snog, and isn't that what Ginny did with her other boyfriends [whom she never stayed long with]? And if their love is meant to last eternally (insert gags at will), why did it seem like JKR was trying to make us hate it?
5) R/Hr, sexual tension? What with all the hand-grabbing, worrying, and being in close proximity under the Invisibility Cloak, I'd say Harry and Hermione have more than their fair share.

6) R/Hr was never officially announced. All the jealousy, public snogging (not with each other, thank God!!), attacks of mad canaries, and twice as much arguing as usual ended in them both crying together.
Really stable grounds for a lifemating situation. It just screams meant-to-be. *gag*
7) Where was the foreshadowing for all this? It's like we don't know the characters we've come to know, love, and admire! I argue with my guy friends all the time but it doesn't mean we have unresolved sexual tension. And how many people never notice the existence of the person destined to be their significant other for six years, especially if their supposed eternal love is the little sister of their best friend?
8) Harry is not the type of person to want someone with a history of instability, little distinguishing personality, and only good looks to her name. Wouldn't you think he'd want definite support with all the bad stuff in his life already? And who's always been there for him? Hermione.
9) Hermione is a more likely target than Ginny (she's smart, very close to Harry, more likely to find the
cleverly hidden Horcruxes than anyone, and he would be terribly devastated if she was lost), so why shouldn't Ginny come along to hunt for Horcruxes? It's the perfect setup for Harry to forget Ginny and find comfort in Hermione. JKR does not take good care of her "good" ships - she allows them to become rusty and ill-used. Way to foster love, care, and romance!
10) Hermione Potter sounds a hell of a lot better, doesn't it? Hermione Weasley...no offense really, but it makes Hermione sound like a weasel.