I can't create an iCloud email.

TL;DR: GO TO ICLOUD.COM AND TOGGLE THE TIME ZONE.

So I called Apple and the nice man from Australia told me to make sure the time zone was set correctly in the iCloud.com settings.

(Log into iCloud.com, choose Account Settings)

But the time zone was already correct (Pacific).

So I toggled the time zone to Mountain. Logged out. Logged in. Changed the time zone back to Pacific.

Then the iCloud mail immediately worked (without me having to go through the creation process again, or anything)!

I'm closing this ticket.

I just updated my operating systems on my MBA and my iPhone. I still can't create an iCloud email address. HELP! :)

Thank you for the wonderful advice, but the fix I described, toggling the time zone in iCloud, is the exact solution for this problem.