>Why did Thrall put Garrosh in charge
Why indeed.

Thrall - an Alliance plant - led the Horde into wars in Outland and Northrend with the intention of most of the orc population dying, as were his orders from Alliance High Command. However, the campaigns were more successful than intended, and the Horde was rivalling the Alliance in terms of power and might by the end of the war against the Lich King.

Alliance High Command devised a new ploy to destroy the Horde: by installing a certified retard as leader. They decided to retire Thrall as Warchief and let him live out his days under a witness protection program in Nagrand, while installing Garrosh - who was by all accounts too inexperienced and too rash to be a leader - as Warchief. Remember that Garrosh is unaware of these schemes and believes he is doing what is best for the Horde. He is also unaware that Thrall is an Alliance asset.

The Alliance - known allies of the Grimtotem tribe - contacted their agent Magatha and devised the Thunder Bluff coup and the events surrounding it, with the intent of turning the tauren against the orcs, which succeeded. Garrosh, learning that Magatha is an Alliance asset, condemns her and orders her death, but the damage has already been done, and Baine and the tauren are now anti-orc. It is also around this period that the Alliance recruits Vol'jin as an asset.

Fast forward a year and Garrosh is increasingly unpopular as the invasion of Pandaria continues. Garrosh asks his spies to investigate why his Horde leaders are turning against him, and discovers that Vol'jin is an Alliance asset who is scheming against him. For the good of the Horde, Garrosh orders Vol'jin's assassination. However, Vol'jin is rescued and rendezvous with his Alliance handler Tyrathan Khort.

You know the rest. The Alliance launches a rebellion, Garrosh is deposed, and Alliance asset Vol'jin becomes Warchief.