Some of those objections disappear if you treat the father's advice as a heuristic and not an absolute rule - something like "being able to cook and keep a house clean increases your chances of finding a desirable long-term partner"; especially objection 2 (I would expect a woman would also prefer a partner who can cook and keep a house clean, all else being equal) and 4 (even if some men are perfectly okay with a wife that can't cook, I would expect that all else being equal being able to cook still makes one a more desirable partner).

"There are exceptions to that rule" is close to a fully general counterargument, because there are exception to pretty much any rule (outside the hard sciences), and I'm a bit annoyed when such an exceptions is used to triumphantly "refute" an argument (for example "once there was this guy who would have died if he had been wearing a seat belt!").

I do agree that the statement is sneaking in some iffy connotations like "your value as a woman is who you marry" and "you don't pick a husband, you get picked", and even if knowing how to cook does make increase the chances one ends up in a happy long-term relationship, other traits probably have more bang for the buck.