Edit: Basically you have to control for what's causing women to work less when the have children. And the obvious answer is because if you're a woman it's hard to work when you have a child at home. If you're a man that's not really true since typically your wife/girlfriend takes care of the child. You can argue that maybe men should take more responsibility for raising their kids, but that's more of a social/political issue than an economic one.
Just as if I chose to go live in the wilderness, it would only make sense that my income would drop. No one would be at fault and I wouldn't expect the government to make up the difference for my "lost" income.
Your first paragraph applies equally to men - but men are statistically less willing to sacrifice extra income to focus more on familly. Maybe men should not have children (?!).
Nevertheless, ignoring judgemental moral in previous paragraph, it does not make theoretical "men with children earn less" something that needs to be discussed as not economics.
I generally agree with this line of thought, but you're also missing the higher level question: why, in our society, do we have to control for women who have children, but we don't have to control for men who have children?