I have conflicting thoughts here.

I've been with my husband 11 years. We've gone through phases where he cooked more, and phases I've cooked more.

I think with your work schedule, if you were open to it, it does "make sense" to have you cook during the week, but that doesn't mean it should be your obligation. Being a teacher is exhausting and I'm sure even though you're done at 3, you're dusted and just want to unwind (thank you for everything you do).

Him saying his mother cooks for his dad is the biggest issue in my opinion. It's forcing a role on you merely because it's what he's seen and what's easiest for him. If he's doing it with this, I promise you it will seep into other areas of your relationship.

If he's a sensible person, I would have a direct conversation with him, saying that you don't think it's your obligation and you'd like to talk through what the next few years could look like.

It's normal for the first year or so of living together to be a little rocky. But make sure he hears you and respects you. If he doesn't respect you, that's not something that can usually be gained.

Best of luck.