Turbo Tax is calculating all of my American Opportunity Credit as "Non-refundable" on form 8863. Why would it not calculate any portion of that as "Refundable"?

The usual reason for that is that you have indicated that you can be claimed as a dependent on somebody else's tax return (usually you parents) and that they are not actually claiming you and/or you are a full time student, under 24 who does not provide more than half their support with your own earned income. 

While technically there is a provision that allows your student-dependent to claim a federal tuition credit, from a practical matter it seldom works out.  A student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) if he/she supports himself by working. She cannot be supporting herself on student loans & grants and 529 plans and parental support.  It is usually best if the parent claims that credit.  

If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition 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 he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable)

https://ttlc.intuit.com/questions/3936383-tuition-gift-to-children

https://ttlc.intuit.com/questions/4531097-just-because-i-can-claim-a-college-son-daughter-do-i-need-too-they-live-on-campus-and-i-provide-rent-but-that-could-be-a-gift-i-don-t-get-any-benefit-claiming-them