Well, it starts with the first and second war.
Hyped up on demon blood, the Orcs committed some extreme atrocities and laid waste to much of the world. After the blood frenzy subsided, they were left with the weight of the decisions they didn’t fully make. No amount of “I’m sorry” is going to fix that and the concentration camps were evidence of that. With no way home (and the one time it was open, they couldn’t remain on the account of the planet slowly dying), the Orcs strive to carve their way out on this planet.
The Trolls have long been butting heads with the mortal races of the world. The Orcs just fell in with them.
For the Forsaken, the Forsaken have had the displeasure of being risen into undeath and even once free, their former countrymen turned arms against them and thought them monsters. On top of occupying their old homes - much to the survivors of Lordaeron’s displeasure, who thought themselves the rightful inheritors of their kingdom - there was the added threat of hostilities in their formative days, when they were sending diplomats to both the Horde and the Alliance, only for those who made the travel to Stormwind never returned. It’s been game on between them and most of the world for awhile now.
I think the only ones who weren’t under the crosshairs were the Tauren and the Blood Elves. The Tauren owed much to the Horde for springing them from the perils of the Centaurs and fell in with the Horde to both survive in a hostile world and offer their assistance for aid given.
The Blood Elves were rallied Kael’thus and needed allies in their lonely spit of land in northern Eastern Kingdoms- who better to be good neighbors than the Forsaken and, by extension, the Horde they’re rallied in.
Although the armies of the Alliance and Horde have grown enough in strength to stave off war (for the most part) by deterrence of strength and things have seen less dangerous between the two kingdoms, the danger hasn’t really left, with the forces in Durotar and the Barrens being a firm message that, if they could take military action, they would.
If you’re looking for more recent acts of aggression, the Alliance attempts to colonize the Western Plaguelands- a territory in the literal back yard of the Forsaken- and move in an army to Andorhal to try and claim it. That’s just a sampler.
This isn’t to say the opposition doesn’t have some valid grievances, but, there is no other option for the Horde. Survive and thrive, or bend the knee and die. The world they find themselves in is very much not safe to them.
EDIT: Oops. Made some 4 AM typos.