I never felt like garosh was a belivable character. His hatred for the alliance was completly unjust. I mean the alliance did literaly NOTHING to piss him off. I mean I would get it if he wanted to rule the world of whatever, but his hatred of King varyian at the dalaran negociations, plus other outbursts showing pure hatred towards the alliance just shows poor character development.
So lets see what the horde did vs what the alliance got since the start of w3
-Killed everebody at wrathgate (well not horde per say, but a rogue faction so for the alliance it would look like the horde did it)
-Pissed off King Varyian on several ocasions.
-Stole the bell from Darnassus
Now lets look at what the alliance did
-Destroyed camp Taurajo
-Imprisoned the blood elves from Dalaran (I doubt garosh really cares)
In the story "Heart of War", Garrosh learned that Northwatch and Bael Modan contested Horde sovereignty, the humans of Tiragarde robbed from Razor Hill in a land with few resources, and the night elves ambush lumber caravans. Garrosh became determined to bring glory to the orcs again after he saw the shame they carry from their greenskin, and in his eyes, the Alliance, as the enemies of the Horde, needed to be crushed for that to happen.