Excerpts from Books and Wikipedia
"In the role, Thomas showed himself to be devoted to the king's interests; he was efficient and hardworking, especially in the raising of taxes. Henry clearly thought that Thomas would continue to serve him in the same way once he became archbishop, but the king was soon proved wrong. . . . However, when Becket resisted Henry's demands that 'criminous clerks' (priests who had broken the law) should no longer enjoy the privilege of being tried only in ecclesiastic courts, the rift between them deepened to such an extent that in 1164 the archbishop fled abroad and all attempts at reconciliation failed." [1001 Days]