Why the amount on my 1098T line 1 didn't reduce my federal tax due?

An education credit would likely reduce your federal income tax. You may not be entitled to one for several reasons. Likely reasons would be that you can be claimed as a dependent on someone else's tax return, you are not enrolled at least half-time in school,  your income is too high ($90,000 single filer or $180,000 joint) or your scholarship income reported in box 5 on your form 1098-T is more than your tuition reported in box 1.

Also, if you are a graduate student, you can only use an education credit to reduce your tax to $0, so if your income was minimal you may not have any tax to generate the credit.

You can read more here:

Education Credits

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.

Reference: Line 7 instructions for form 8863. https://www.irs.gov/instructions/i8863

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

https://www.irs.gov/newsroom/american-opportunity-tax-credit-questions-and-answers

https://www.irs.gov/credits-deductions/individuals/education-credits-questions-and-answers

 https://www.irs.gov/individuals/llc