Why don't I qualify for the American Opportunity tax credit when I'm a full time student, no one claims me as a dependent, and I make very little money?

[Hal_Al]

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 (AOTC) if he supports himself by working (unless you're an orphan). 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 a 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

If you are not claimed as a dependent, even if you could be, you are allowed the non refundable portion of the AOTC.  But, if you make very little money, it's unlikely that you will have a tax liability to take the credit against.