Right. But the whole point is that if you have just been handed a newborn then your option to 'walk out' is simply non-existent and so any principled stance would have to be postponed until the breadwinner is out of the danger zone. The employer here seems to be engaging in some kind of revenge tactic, as though the leave was to be made up for rather than something that left the balance between employer/employee and employee/co-workers in tact.
So I don't see this as a request at all, a request is something that you practically can say yes to, which doesn't appear to be the case here and does not come in the form of an order.
Again, saying no to a request to sacrifice all your nights and weekends for a month is not the same as quitting your job. It's certainly not a fireable offence.
They do indeed have places where an employer can reasonably ask an employee to sacrifice his entire life for the company. Those places are nearly all called "Japan", and the employer/employee relationship is very different to that in the USA.
Try enslaving your workers here (or firing them for refusing to be enslaved), and you face an unpleasant lawsuit.
So I don't see this as a request at all, a request is something that you practically can say yes to, which doesn't appear to be the case here and does not come in the form of an order.