That may be how the laws are written, but that isn't how they're enforced in practice.
Divorces are initiated about 70-90% by women (I've seen numbers quoted throughout the range depending on the time period and the demographics being looked at), women end up with the kids 80-90% of the time, and so on. Almost all spousal support is awarded to women. And so on.
The usual argument about the kids ending up with the mother because the father doesn't want more time with them is often offered without much questioning, but the same people that argue this would not so easily accept similar arguments to explain differences in incarceration rates between people of different ethnic backgrounds, for example.