Blimey! He's telling you clearly that he believes that if you were to have children together in future, you would be the carer, home-maker etc (whether or not also working FT) because that's the way it is innit.
That's what his reference to your parents means. 'That is the way it is and ever will be thus'. So, by all means dabble in feminism now, while you're young, play at being equal in the workplace but, when children come (if not before), Kaboom! 'Housewife and mother' you are!
He is not at all unusual in thinking like this. Many, many people hold an idea in their mind of 'mother' which encompasses all or most childcare and housework. Even if they grow up with ideas of equality, this concept does not disappear, it just fades temporarily. Cognitive dissonance, unexamined assumptions, whatever. It is real. It lurks, then asserts itself at the relevant moment.
So it's really quite helpful of him to have been so upfront about this. You have the opportunity to talk and work through it with him. Or to leave him, if you think or find him unmoveable on this (and probably a whole heap of other sexist assumptions and ideas).
On the one hand, he may be being naive and may be young enough that he can change (note - he can. You can help, talk, gain life experience together but you cannot change anyone else against their will). Or, he may actually be an entrenched mega-sexist with a very thin veneer of equality, or of 'tell her what she wants to hear'.
In many ways, the more difficult and disppointing men to deal with are those with a thicker veneer, who actually believe their own lines when younger, so are convincing and seem reasonable. Until parenthood happens and the unuqual behaviour kicks in.
Anyway, you should both learn to cook. It's an essential life skill for people - all people.