"As an 18-year-old, your parents have no legal right to talk with your professors without your permission"

The parents can talk to anyone they want, with or without any third party's permission.

What's prohibited is the professor disclosing to the parent, without written permission from the student, certain of the student's education records.

And it's not just for 18-year-olds. It's also for any student who is "attending an institution of postsecondary education". A 14-year-old who has graduated from high school and is now attending Harvard has the same privacy rights as a 24-year-old. The student's permission is required before information may be disclosed to the parents.

FERPA (20 USC 1232g)