According to the information on the verification form (at https://www.att.com/verification/teacher):

Certified/licensed K-12 teachers and college/university professors and instructors may be eligible.

Do you fit either the Certified/licensed K-12 teacher or the college/university professor/instructor category?  That's a hard requirement.  

Is your employer one of the organizations listed in the "Where do you work?" drop down on that page?  If not, it may make it difficult.  A contract employee vs a independent contractor may also be an issue.  Did you fill out this form?

My husband just retired after 40 years as a university instructor. Would he qualify?

Active certified/licensed K-12 classroom teachers and college/university professors and instructors based in the U.S can receive discounts. 

studying at home is especially relevant during the pandemic, so do what you love under any circumstances

Home School Teacher

My husband and I contract each year with the local school district in order to teach piano to home school students. I am having trouble getting AT&T to accept this for the teacher discount. 

This year I also had similar problems. I'm a tutor and I don't have a license. So far I have not found a way to solve the problem. But I hope to come up with something or find information on this forum.

@MickeYX , I'm not sure what "problem" it is you are trying to solve.  AT&T offers the discount to "Certified/licensed K-12 teachers" and a tutor is not either.  Whether you consider that "fair" or not, that's the way the discount is designed.