To clarify, you can't remove the address you created when you opened the account - @mac.com, @me.com or @icloud.com depending on when you did this - and you can't remove the other versions if you have them: for example if you started with an @me.com address you automatically got an @icloud.com address as well when iCloud opened, and this gets confusingly referred to as an alias.
An 'email alias' is an additional address which delivers into the inbox alongside the main address(es). These can be deleted, but not used as a login or to create a new ID. I wondered if it was one of these which you provided your daughter with. As Eric says, the '?' or 'X' indicate whether you can delete the address or not. These show on the iCloud website, not the Apple ID website.