First disclaimer: I never read past the first volume of the Ouran manga (although I know it's the endgame pairing in that) or watched past episode 20 or so of the anime. Second disclaimer: I don't actually hate this pairing. There are just aspects of it that make me very uncomfortable that most of the fandom seems to overlook or squee over.
The core of it is that I feel like treating Tamaki/Haruhi as a serious pairing, as the pairing of the series, validates all the (often sexist) cliches of shoujo that the series professed at first to be satirizing. When Tamaki declared himself to be the romantic hero and all the other guys the "homo side characters," it was funny at first, and then it was uncomfortable, because the text backed him up in that bullshit instead of following through and really turning it upside down. And that's just one example. Another issue is that when Tamaki goes into potential-boyfriend mode around Haruhi, he imposes all sorts of sexist expectations on her, rather than accepting her as the slightly genderqueer, androgynous person she is. But for me that's secondary to the main issue, which is that the series uses Tamaki/Haruhi as a vehicle to joke about sexist cliches in shoujo...then turns around and treats it as the serious pairing of the canon.
That said, I really like them as friends, and they do have chemistry. Haruhi is the one who sees through the illusions, and Tamaki is the one who makes the illusions real. They surprise and improve each other in interesting ways. I even don't mind it as a pairing sometimes. I just don't like it, from what I've seen and read, as the pairing of the series.
Day 02 - What was your very first ship?
Day 03 - A pairing that needs to happen now?
Day 04 - The pairing with the most chemistry?
Day 05 - The pairing with the least chemistry?
Day 06 - The best kiss?
Day 07 - The most heartbreaking scene?
Day 08 - The pairing with the most baggage?
Day 09 - The most believable relationship?
Day 10 - Why aren't these two married in real life?
Day 11 - What is your dream pairing?
Day 12 - Who had the best wedding?
Day 13 - What is your favorite television pairing?
Day 14 - What is your favorite book pairing?
Day 15 - What is your favorite real life pairing?
Day 16 - What is the absolute worst pairing?
Day 17 - A pairing you thought would never work out, but did?
Day 18 - What is the cutest pairing?
Day 19 - A pairing you've rooted for since the beginning?
Day 20 - The "can't stand the sexual tension anymore" pairing?
Day 21 - A pairing you like and no one else understands why?
Day 22 - A pairing you hate and no one else understands why?
Day 23 - A crazy love triangle/quadrilateral that worked out great?
Day 24 - A crazy love triangle/quadrilateral that worked out badly?
Day 25 - A pairing that was/would-be adorable, but could never work out?
Day 26 - A pairing that you hated and ended up loving?
Day 27 - A pairing that you loved and ended up hating?
Day 28 - A pairing that you will never understand?
Day 29 - What ship had the best proposal?
Day 30 - Your favorite ship forever and ever and ever?