You can claim the education credit for qualified education expenses paid by cash, check, credit or debit card or paid with money from a loan.

You must be considered an eligible student:

• You're enrolled at least half-time in a program leading to a degree, certificate, or other recognized credential.
• You had at least one academic period beginning during the year.
• You did not use the American Opportunity Tax Credit for more than three previous years.
• You didn't complete the first four years of post-secondary education before the beginning of the year.

Here are other common reasons you might not qualify:

• You're filing your return as Married Filing Separately.
• Your adjusted gross income (AGI) is too high.
  • American Opportunity Tax Credit AGI limit is $90,000 ($180,000 for joint returns).
  • Lifetime Learning Credit AGI limit is $65,000 ($130,000 for joint returns).
• Your expenses were paid with tax-free scholarships, fellowships, grants, education savings account funds, tax-free savings bond interest, or employer-provided education assistance.
• Someone else, such as your parents, list you as a dependent on their tax return.

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 may only be you are looking in the wrong place. The non-refundable portion shows on line  3 of schedule 3 (line 50 in 2018) and will be blank if you had no tax liability to off set. The refundable portion (up to $1000 will be on line 18c of  form 1040 (line 17 in 2018).

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 unmarried  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. 

You cannot claim a credit if you are, or can be, claimed as a dependent by someone else. There is a limit of claiming the AOTC a total of four times (4 tax years) per student, whether claimed by the student or his parents. You cannot file as Married Filing separately.

Go thru the interview again. In particular, Edit your personal information at the beginning of the software. When Turbotax (TT) sees from your birth date that you are under 24, it specifically asks if you provided more than half your support with earned income.

Also see this TT FAQ https://ttlc.intuit.com/questions/3383321-why-didn-t-i-get-a-credit-or-deduction-for-education-expen...