Can’t find the option to turn off two-factor authentication?

Apple removed the option to turn off two-factor authentication on some Apple IDs created in iOS 10.3 or macOS 10.12.4 and later.

In such a case, you have three options:

1. If you recently enabled two-factor authentication, however, you can unenroll for a period of two weeks. Just open your enrollment confirmation email and click the link to return to your previous security settings. 
   
2. Contact Apple support and ask them to disable two-factor authentication for you.
3. Register a New iCloud ID on Apple website and change the iCloud ID on the iPhone. (You can keep the old Apple ID for App Store on the iPhone)

Create a New iCloud ID

Go to https://appleid.apple.com/account#!&page=create to create a new iCloud ID. Verify your Email after signing up. (1,2,3)

Switch to a New iCloud ID without changing the current Apple ID for App Store

1. Go to Device Settings > Apple ID, scroll down to tap on“Sign Out” > “Sign Out of iCloud”, input the password, and tap on “Turn Off”. (1,2,3)
2. Choose the data types to be kept on the phone, then tap on “Sign Out” on the top right.
3. On Settings > Apple ID, tap on Apple ID, select “Not [email protected]“, and input the new iCloud ID and password. (1,2)
4. Then you have switched to a new iCloud account successfully. The two-factor authentication is disabled.
5. On Settings > Apple ID, tap on the newly added iCloud ID and enable iCloud Backup. (1,2)