The usual reason, you can't claim it is that your income is too high ($90,000 single $180,000 Married).
The student can't claim it because congress wrote the law to benefit parents.
A full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. It is usually best if the parent claims that credit.
You cannot claim the (up to) $1000 refundable credit if you are, or can be, claimed as a dependent by someone else.
Reference: Line 7 instructions for form 8863.
https://www.irs.gov/instructions/i8863#en_US_2024_publink53002gd0e674
If the student actually has a tax liability, there is a provision to allow her to claim the non-refundable credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. The student must still indicate that she can be claimed as a dependent, on her return.
