he has no shortage of enemies, but lets stick to the main ones. Can pick other if you think someone else does.
Varian: Garrosh crippled his son and is hell bent on destroying his faction. They've fought to a draw 3 times and another fight is expected.
Thrall: Garrosh ruined his faction. Garrosh constantly undermined him. Garrosh is also HIS mistake.
Vol'jin: Garrosh tried to have him murdered. Garrosh put his people under oppression and held them hostage in tides of war.
Baine: Garrosh killed his father. See above in tides of war.
Jaina: Garrosh destroyed Theramore and killed a ton of Jaina's friends and people.
Lor'themar: Garrosh sent BE soldiers to their deaths more than once, and had no regard for a sha attacking Silvermoon. he also talked smack to lor'themar's face about the Scourge invasion of Quel'thalas.
Tyrande: Garrosh tried to have her assassinated. Garrosh targets her and her people more than any other race, and has invaded her land as far as Darkshore. He also wants to expel the NEs from the continent, but settles for genociding them instead.
Sylvanas: Garrosh uses her people (who according to her are her "body and soul") as fodder. Also the bitch line.....
Gallywix: Garrosh is likely to bankrupt himself in the war? (yes Im reaching)
Saurfang: Saurfang promised to end him if he went too far. Leading to the horde to ruin, sha consumption and rebellion is pretty far.