I am confused why my wife working while being a full time student is lowering the childcare credit, I can't find any reason in section 503 of the tax code. Why is that?

The size of your child care credit is based on how much you spend for child and dependent care, as well as your income. The higher your income the lower the credit.

This link to the TurboTax help page The Ins and Outs of the Child and Dependent Care Tax Credit has information that you may find useful.