But they don't, at least not equally. The only parenting task that men, on average, spend more time doing than women is driving the kids places. Otherwise, women shoulder the vast majority of the effort, regardless of employment status.
No, you shouldn't expect this. The vast majority of talking pundits on TV are male. There's a reason for this. And when you do see a woman pundit, most times there's a nanny or childminder with the kids.
"Can easily" doesn't mean "will".
How many facts do you need? There is a huge body of academic research on gender roles in society. Ignorance of this research is ignorant.
The details of the family are tangental. The article I pointed to was about societal norms and attitudes.
We all have a right to criticize societal norms and attitudes, and, arguably, a duty to work to change them when equity is at stake. But I think that's not what you meant, when you were hastily missing the point.