To log out you must first add a recovery method to your account.

You can do this by going to Settings > Account  and add an ATA ID/Facebook Link.

How do I log out?

STEP 1 -  Go to  Settings -> Account  -> Devices  and tap DISCONNECT.
account screen

STEP 2 - Tap Continue on the first pop-up.
disconnect warning1

STEP 3 - Tap Continue on the second pop-up.
disconnect warning2

The game will  take you to the New Account Screen where you can create a new account or recover access to an existing account through ATA ID/Facebook by tapping Log In.