Originally Posted by The_Yearning
Because Tywin is the Hand of the King (and if you have been paying attention, it's practically Tywin running the show). By signing Loras to the Kingsguard, he would never be able to marry, and even though Margery would be married to Joffrey, she's nothing but the queen.
I understand about the kingsguard, I remember the whole thing with Jaime, but I was under the impression that you had to volunteer for it. Moreover you would think a powerful family like the Tyrells who control one of the 7 kingdoms could resist.
Also Sansa is believed to be heir to the North, so she is an extremely valuable commodity.
EDIT: has it been established that the Reach (Controlled by the Tyrells) is the most agriculturally fertile region of Westeros and allows the Tyrells to be one of the richer houses and field the largest armies? Were the Lannisters somewhat dependent on their alliance?