A more subtle point is that the incentive structure for men to work had has evaporated. In divorce (which is largely initiated by women), men stand to lose more in alimony and child support. The economics say that if you marry (and far more people decide not to do these days), you probably shouldn't be the sole breadwinner and you certainly shouldn't earn more than your wife.
I know a number of couples where the man just doesn't work and is supported by his wife. I don't think it's a conscious choice, it's unconscious and based on incentive.
I might be wrong, but something like 4% of divorce cases have custody determined by the court, so that's a decision made by fathers (I have custody of my kids, and had no problem getting it, FWIW).
True, but it's not a choice made in a vacuum. Often the context is: I'm the only one making enough money to support the kids, so I have to work for this to work out at all, and I can't afford day care. So for the sake of the kids the mother gets custody. "Choice," true---but not free and uninfluenced, as you imply.
I know a number of couples where the man just doesn't work and is supported by his wife. I don't think it's a conscious choice, it's unconscious and based on incentive.