I spent half an hour trying to resolve and figure this out, then another hour with support before I realized a simple solution.
This morning I restarted my Mac and it obviously ran an update for Creative Cloud and signed me out of everything. When I attempted to open Illustrator it asked me to login so I put in my email address and his "Continue" but it did not/would not proceed to the password or authentication page. This was happening on all apps/Creative Cloud AND the website on my Mac (Chrome, Firefox and Safari).
Long story short I ran the cleaner tool sent by support, accidentally removed everything (which I wanted to start from scratch anyway) and then was unable to login still after going through Support's suggestiong.
You will need to login from a Windows device and once you have, go to your account and select to Connect Accounts (Apple, Facebook, Google). Select one of these and you'll be able to login on your mac by that connected account.
Hope this helps someone, seems like a possible development issue for Mac on Adobe's end? I've seen a few others experience this issue very recently.