He did not develop it, he helped implement it.
I don't try to understand why he pushed that, as it is completely backward from what he represented.
But he was a great man, even with that error.
"Friedman contributed to another important effort while in Washington during World War II. At the Treasury Department, he helped create the current federal income tax withholding system. Friedman says he now regrets his role, although at the time he believed the new system was superior to the one it replaced (Friedman and Friedman 1998, 123). Working in Washington gave him great insight and the chance for a firsthand look at how bureaucracies function. http://www.dallasfed.org/research/ei/ei0202.html