How did Luther "mislead" the peasants? Why did they expect he would support them? What was his reaction?

Luther's Reformation unleashed a lot of unforeseen revolutionary social and political forces that soon got out of hand. Luther himself was quite conservative politically, believing that secular rulers were appointed by God and, as such, were deserving of the absolute obedience and loyalty of their subjects. The Reformation, among other things, represented an assault on the power and authority of the Catholic Church, so it's not surprising that many people saw an opportunity to extend the Protestant principle from religion to secular politics and society.
Suitably inspired by the spirit, if not the letter, of Luther's teachings, large numbers of aggrieved German peasants staged a full-scale revolt against what they saw as rampant exploitation and injustice at the hands of the social and political elite. They thought that Luther was on their side. After all, here was someone of peasant origins himself, a man who had bravely challenged the power and authority of the Catholic Church.
Sadly for the peasants, they were to be disabused of such notions. Not only did Luther fail to support them, he published a furious polemic entitled Against the Thieving, Murderous Hordes of Peasants. Never one to mince words, Luther viciously attacked the peasants for their violent uprising against what he regarded as the divinely ordained forces of law and order. He also openly encouraged the princes and other secular rulers to suppress the peasants' revolt with the utmost ruthlessness. Although the language used by Luther was, even by his standards, intemperate in the extreme, we should bear in mind that he thought the peasants were acting against God's will by revolting against the very princes that the Almighty had appointed to rule over them.
The princes duly suppressed the uprising, often resorting to extreme violence to crush the peasants. For those peasants who survived, Luther's intervention on the side of their oppressors was a total betrayal of the spirit of the Reformation, with its radical assault on authority. They didn't share Luther's complete separation between the secular and the religious spheres; to them, everything was linked. A number of other Protestant sects, such as the Anabaptists, preached a similarly radical social and political message, but they would always be regarded by Luther with the same degree of suspicion, hostility, and downright contempt that he reserved for the rebellious peasantry of the German lands.