AOC not eligible for refundable credit

No.   You can be claimed as a dependent by your parents if you did not provide over half of your total expenses (support) for 2021.   $25K is probably not more than half.   When determining if you supported yourself, you have to include in your expenses - all of your tuition, student room & board, housing costs while away from school, food, medical costs, clothing, recreation, travel and transportation costs, etc.   Your parents do not have to provide half of your support, but in order for you to claim yourself, you do have to have paid for over half of those expenses with earned income to be considered NOT a dependent.  

A full time unmarried student, under age 24, whether a dependent or not,  is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself with parental support, 529 plans, student loans, gifts, grants, or scholarships.   You usually must have actually paid tuition, not had it paid by scholarships & grants.   It is very rare for students to qualify for the refundable portion of the credit.   

It is rare, but possible - To be eligible, you would have to indicate that you CAN'T be claimed by anyone else - and that you provided more than half of your total expenses with earned income.   Both of those questions are in the Personal Info section.   

When TurboTax sees that you are a FT student, under 24, it will add an earned income support question to the interview . The earned income support question is part of the personal info interview, not  the education interview.

Go thru the personal info  section again and be sure you answered that question correctly (or you answered the preceding questions correctly to generate that question).