Using previous alternate email as apple id

According to Apple's support page:

1. Go to My Apple ID, click "Manage your Apple ID," and sign in.
2. Delete the alternate email that you have. Click Yes when it asks for confirmation.
3. With the Name, ID, and Email Address drawer selected, click Edit next to Apple ID and Primary Email Address.
4. Enter your new email address.

I just applied the following steps above to my own Apple ID and it did not complain.

I had the same issue, but I found a solution!

There are 2 separate sets of safety emails, an "alternate email" in the name, ID, and email addresses section of AppleID and a "rescue email" under password and security.

I only deleted the email I wanted to make my primary as an alternate email, not realizing that it was also my rescue email. After deleting it as my rescue email it was no longer associated with my AppleID and I could make it my primary.