The Feminist Line:
Equal access would chip away at a mother's right to parent her own children.
The target of this argument is the father; aka, the other parent. In intact families, father's have the right and responsibility to parent their children as much as the mother. So, whether working 80 hours, 7 days a week in the coal mines or staying at home while the mother earns living wages, both parents should have equal access to parent their children. The argument turns on itself.