Why are the orcs turning on Garrosh? Isn't he the best warchief they ever had? Oh, I understand why the other species in the horde might not be so happy with him, but why would any real orc care about those wusses? Lok'tar Ogar, and all that.If we're talking story, the orcs generally aren't turning on Garrosh. Which is why we're besieging Ogrimmar.
As for players, I think that Horde players see themselves first as Horde, and second as an orc, troll, tauren, etc. So they oppose Garrosh for damaging the Horde as a whole.
I saw an interesting question today: Why do players hate Garrosh, but like Sylvannas? You can make a case that Sylvannas is morally worse than Garrosh, what with the plague and the val'kyr. Yet Sylvannas is still a clear favorite with many players.
My first thought is that it is because Garrosh is a jock, and Sylvannas is a nerd. Garrosh is a thug, with lots of shouting and physical intimidation. Sylvannas is all cool and calculating. Since the playerbase draws extensively from the nerd/geek subculture, which is pretty hostile to the jock subculture, their sympathies are with Sylvannas.
What's sometimes lost is that Garrosh is pretty effective as a warleader. He's conquered most of Kalimdor. The strike on Theramore was tactically brilliant. He took out the main Alliance stronghold on Kalimdor, and killed many high-ranking Alliance officers. He almost took out Jaina Proudmoore, which would have been the one of the greatest Horde victories. Not to mention that if Jaina had been killed, Dalaran would have almost certainly fallen to the Sunreavers, as both Rhonin and Jaina would have been dead.
Yet if you asked the players which type of villain they would be like, the vast majority of players would choose the cool, calculating intellectual style of a Sylvannas. They look upon the rough, physical style of a Garrosh with distaste.
Still, the greatest crime of Garrosh is not Theramore, but the death of Cairne and the treatment of the other Horde races. It would have been interesting to see a Garrosh who took the exact same actions towards the Alliance, but chose to bind the Horde together instead of dividing it. A Garrosh who gave Vol'jin command over a theatre of war like Sylvannas, instead of attempting to assassinate him.
I think that if Garrosh did that differently, but everything else the same, including nuking Theramore and despoiling Pandaria, I think the great majority of the Horde would have been happier with him as Warchief, even supporting him over Thrall.