Because Congress said so when they wrote the law.
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 student, under age 24, 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 must have actually paid tuition, not had it paid by scholarships & grants. It is usually best if the parent claims that credit.
He cannot claim a credit if he is , or can be, claimed as a dependent by someone else**.
**But there is a provision that allows the student to claim some of the tuition credit himself. If the student actually has a tax liability he can claim a non-refundable credit. But then the parent must forgo claiming the student's dependent credit and the student still can’t claim himself.