Add an email address to my Apple ID Reachable AT section

iMac running mac os 10.13.6

I want to add an email address to my Apple ID Reachable AT section. The system replies: This email address is not available. Choose a different address. The email I want to add is my primary address. Any ideas about why this is and, more importantly, how to fix it?

Thanks!

[Re-Titled by Moderator]