I am under 24, and not a dependent on anyone's taxes. I was a full time student in 2020 and qualify for the American Opportunity Credit. Why am I not getting this credit?

If you are eligible, you have answered  something wrong, in the interview. But, a lot of people are just not eligible. See https://www.irs.gov/Individuals/AOTC It could be that last year was wrong. 

There's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. 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. You usually must have actually paid tuition, not had it paid by scholarships & grants.  It is usually best if the parent claims that credit. 

You cannot claim a credit if you are, or can be, claimed as a dependent by someone else.

*If you are under 24, in the personal info section of TurboTax (not the education section) you will be asked if more than half you support comes from your earned income. You must answer that question yes. 

Reference: Pub 970, page 21 https://www.irs.gov/pub/irs-pdf/p970.pdf

If you are eligible to be a dependent on a return, you can not claim the credit, even if your are not claimed. 

Look at this link and scroll down to the instructions for line 7: Instructions for Form 8863 

Since you are under age 24 and a full time student, your earned income must equate to more than one-half of your support.