If I am a full-time student in Tennessee but a resident of North Carolina, why do I owe North Carolina money on my taxes?

If you live in North Carolina, you must report all of your wages to your state of residence. You will then be taxed on them. If you paid taxes to another state, you can take a credit for those out-of-state taxes to reduce your North Carolina liability. Since Tennessee doesn't have an income tax, any money you made working there wouldn't generate a credit to offset your North Carolina tax liability.

You can read more about living and working in different states here: Multiple States—Figuring What's Owed When You Live and Work in More Than One State