Why isn't TurboTax calculation my tuition in my return?

The tuition and fees deduction is not a refundable tax credit. It is a tax deduction (maximum $4,000) which will reduce your taxable income.

In your case, if you are in the 12% tax bracket, the tuition deduction can reduce your taxable income by $1,917 and your tax liability by $230 (12% x $1,917). If your tax liability is less than $230, it will be reduced to zero, but you will not receive any refund.

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 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