Maybe our society should require home-ec courses for all students with the requirement of a passing grade?
But yeah, agree with you on that angle, successful relationships require division of labor in the household. My cooking epically sucks, so my wife does it (and grumbles), but then on the flip side I chuckle when I tell her no ... laundry includes sorting, washing, drying, folding "and putting it away" ....
You are correct it is about the parenting 100%, but one thing that might help is if the father is the one to enforce the shared domestic labor angle. Boys mimic other boys and men, so that might help out some.