For the most part this is mutual, but the real culprit behind everything is King Varian Wynn. Yes, the human king hates the Orcs (and by extension the Horde) and, to be honest, who can blame him? Abducted, bespelled and sold into slavery as part of a grand plot by the dragoness Onyxia he (as the gladiator Lo'Gosh) found himself without his memories in Orgrimmar.
Now returned to his throne room in Stormwind, he is a changed man. Bitter and battleworn, his attitude only gets worse once the Alliance loses its greatest living legend Bolvar Fordragon during the battle of the Wrath Gate.
So last night, I finally got around to completing the Wrath Gate questline and witnessed for myself how much Varian is letting his hatred rule his head. He blames the Horde and Thrall personally for the death of Bolvar despite the fact that it was a renegade faction of the Forsaken under the orders of Grand Apothocary Putress which caused the massacre. For now, at least, he seems so blinded by hate that he is unable or unwilling to make that distinction:
"I've waited a long time for this, Thrall. For every time I was thrown into one of your damned arenas... for every time I killed a green-skinned aberration like you... I could only think of one thing. What our world could be without you and your twisted Horde..."
At the same time, the Horde are not all innocence and light either. Thrall's right-hand orc Garrosh Hellscream
is just as bad. While he doesn't so much hate humans, he does lust for power seeing himself as the next Warchief and believes Thrall's weakness is his willingness to entertain humans like Jaina Proudmore (who I'm sure Thrall has a crush on).
So with 3.1, we got our first proper look at how the Alliance and Horde are coping post-Wrath Gate and it's not pretty. Varian seems to be swallowed by grief and fury while Thrall is receptive to Jaina's suggestions simply because she has always been a mediator between the factions.
You'd think such a dangerous situation as the resurgence of the Old God Yogg-Saron
might unite these enemies against a common foe. Perhaps in the past this could have been true but now, neither side is willing to be co-operative. The trailer, as well as setting up 3.1, also features a promising sub-plot focusing on how the the two sides are beginning to turn completely against each other. I think it's only a matter of time before Blizzard bring this whole mess to a head and Varian and Garrosh face off.
We've already seen from the trailer that this is part of an on-going storyline, but I suspect it's not just a justification for war. There's a promise of something larger than just one king's grudge and perhaps we will discover an answer in the next patch or expansion.