Of course the party at fault is the man.
It is not victim-blaming, however, to ask why a woman would accept to do the majority of the household chores.
Even when I was early 20s, if a boyfriend had asked me what was for dinner I would have answered that they could take care of it as I did it the day before. Or that I would do it while he does the laundry.
I agree that everything kids related is defaulted to the mum - partly due to the long mat leaves and also because many mums (including me) don’t trust that the dad would do things correctly. It is however absolutely fair to tell the dad that x, y, z are now 100% his responsability. For ex: sports club and kit (organising, paying, buying and washing kit, getting bag ready), cutting nails (noticing when needed and doing it), dentist app, all school correspondance…