The dudes who espouse those views in such black and white ways are typically single dudes who haven't had a girlfriend recently, let alone married with children.
Yes, it's handy for one to focus primarily on the children and the other to focus on income generation/home maintenance but I regularly do dishes tidy the livingroom, sweep floors or whatever else is needed. I can also look after my daughter on my own if I need to.
The balance is pretty fluid. You work as a team to keep the house running. That's what these guys miss.