Let's say both the guy and girl make the same amount of money and are both good at and enjoy cooking and cleaning.

Would it be wrong for a guy to want the girl to give equal contribution financially to the relationship if he's also willing and capable of contributing equally to domestic duties?

If both people worked exactly the same amount of time, with the same commute etc. and also did exactly the same amount of the same chores, that would be the definition of fair. But that is highly unlikely, and very often what one person perceives as doing half of the chores actually isn't but they do not notice because their partner is picking up the slack. Real life is about finding the balance that works for both people involved. A true half half is not possible.

In this same scenario, would it be wrong for him to expect her to cook and clean if he's expected to handle the financial aspects of the relationship?

If he works eg 8-9 hours it would be fair if she also works 8-9 hours in the household. But again, in real life household work, especially if you have younger kids, doesn't end at 5 o'clock. Coming home at 5oclock after 8 hours of work but expecting your partner to work about 10+ hours or even more if you have kids until the late hours of the evening is not fair in the slightest.