One more time:
The exact quote "Spare the rod and spoil the child" is from Hudibras by Butler.
The big difference is that there is absolutely no quote anyone has ever given me that includes daughters or is at least gender neutral. There is also no quote that allows mothers to hit their kids of either sex.
Oh, and that "Spare the rod..." from Hudibras is in this context:
"Love is a boy
By poets styl'd
Then spare the rod
and spoil the child"
It was written by Samuel Butler to mock the Puritans, and even there addressed only hitting boys.
Spare the rod and spoil the child is scriptural, where he probably found it in the first place.