Child care (lack thereof) affects a woman's professional career far more than it does a man's. How is that fair?

Actually ... Who will take time off to care of the child? is a private decision between the couple involved.  

FMLA (and/or state equivalents) are available for both the mother and father.
I know a few couples who have had the husband stay home, due to the wife having higher wages and benefits.

But yes ... if you take more time off than your colleagues, you are going to "pay" for it.
That's generally fair - since you aren't doing as much work for the employer.

Our children are part of us.  So we are going to care for them as we care for ourselves.  I can't see that as being "unfair".  If we repudiate our children then we are repudiating ourselves.  Men may be able to just go off and do their thing regardless.  But we are not able to without paying some heavy personal dues.  Which most of us choose not to.