I am not sure, but it may be that those two emails are essentially synonymous for your AppleID. The @mac.com email is nothing more than an alias to your iCloud email account so both of those two addresses already sign into the exact same AppleID and either can be used to access it.
If you also have an @me.com address too, then it is also nothing more than an alias to your iCloud account and can also therefore be used to login to that same AppleID.
Since if you use any one of those three (@me.com, @mac.com, or @icloud.com) as the primary email, you cannot switch it back to a third party email - so I think the system is hung up on you trying to edit one of those (albeit with just an alternate alias already assigned to that AppleID) and it thinks you’re trying to replace the @mac.com with a 3rd party email? That’s the only reason I can think it errors out with you trying to delete that @mac.com address and not just swapping the existing aliases.
iCloud: About your @icloud.com, @me.com, and @mac.com email addresses - Apple Support