*sigh*
The saddest thing about that is that there ARE some rather complex reasons in WC lore about why the Alliance and Horde came to hate each other. :sadvaultboy:
The Horde and the alliance don't hate each other at all.
Actually they formed an alliance during the second war against the Burning Legion.
Some fanatic orders from both sides (battle around Theramore vs. Burning Blades) continued to fight each other after the basic borders were settled (and still do so until today). Jaina earned some hatred by solving this matters with Thrall directly instead of just shetting (? dunno word) more blood. That's the reason why she "betrayed" her father. The leaders however are not happy with them and the Burning Blades are hunted inside the Horde, rumors say they also pact with lesser demons. (One of the very first quests after meeting THE WARCHIEF could tell you all this.)
You cannot attack the other faction on PvE servers.
About orcs' invasion in Azeroth: There is basically two large opinions.
1) The orcs homeplanet was basically destroyed (wether or not the burning legion was involved here is unkown, as far as I know). Fact, there was not enough "food" for everyone. So Medivh led them to Azeroth, being the last warden and "father of orcs". He wanted them to live in peace but humans attacked, since they feared the ugly beasts.
2) Sargeras already took control of Medivh (In the epic battle between Aegwyn and Sargeras, the latter managed to transfer his spirit into her unborn child upon death) and forced him to open the Dark Portal to weaken the humans.
I think the first explanation is the right one, since Sargeras wouldn't gain anything from "weakening" the humans at all and his kind does not do anything without benefit for himself.