You're doing it though. You're attempting to excuse Varian's words and actions, trying to make it so they aren't what he actually thinks because of this reason or that reason. while accepting Garrosh on the shallow level of his words.
As for Garrosh, the quick and dirty character building
1) Raised his whole life being told how awful his father is and how his father damned his people
2) Thrall finds him, shows him that Grom was a pretty cool guy
3) Garrosh comes to Azeroth, sees the Orcs being (as he percieves it) oppressed and made poor due to the Alliance
4) Sees that Thrall is doing nothing to fight back for his people. This is not the Orc way, the Orc way is to defend your home and provide for your people
5) Garrosh challenges Thrall and leads the campaign in Northrend
6) Garrosh cuts his teeth in Northrend, mainly against an unmistakably evil force.
7) Garrosh is made Warchief, a position he didn't think he was apt for, and then has all of his advisors either get themselves killed or abandon him.
There is a driving motivation behind Garrosh; The Alliance have forced the Horde to live in squalor. The Alliance hates the Horde and views them as monsters. Therefore, the proper Orcish way to deal with it is to undeniably crush the Alliance so they cannot oppress the Horde