If you are eligible, you have answered something wrong, in the interview. But, a lot of people are just not eligible. The interview is complex, because the eligibility rules are complex.
See:
https://turbotax.intuit.com/tax-tips/college-and-education/what-is-the-american-opportunity-tax-cred...
https://ttlc.intuit.com/community/credits-and-deductions/help/who-is-eligible-to-take-the-american-o...
https://www.irs.gov/Individuals/AOTC
You can use this IRS tool https://www.irs.gov/help/ita/am-i-eligible-to-claim-an-education-credit
or https://www.irs.gov/individuals/llc
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. There are income limits ($180K married, $90K single)
