Both me and my wife were full time students at UNT during 2020. I checked no because we had not completed our post-secondary education. Why would it drop our refund? Or should the box be checked yes?

If you are still in undergraduate college then the answer is No.  I have not completed my post-secondary education.

To be able to claim the American Opportunity Tax Credit or the lifetime learning credit (LLC), you must have received the Form 1098-T, Tuition Statement, for you or your dependent from an eligible educational institution either in the U.S. or abroad.

To be eligible for AOTC, the student must:

• Be pursuing a degree or other recognized education credential.
• Be enrolled at least half time for at least one academic period* beginning in the tax year.
• Not have finished the first four years of higher education at the beginning of the tax year.