Two-factor Authentication For Apple ID Not Showing Up

You will need to contact Apple support. Apple has not elaborated on why some AppleIDs cannot enable 2FA, so we don’t know why yours isn’t giving that option.

Availability of two-factor authentication for Apple ID - Apple Support

“While most iCloud users can now turn on two-factor authentication, certain account types may still be ineligible at Apple’s discretion.”

Here's how to turn on two-factor authentication in Settings (If you're using iOS 10.3 or later):

1. Go to Settings > [your name] > Password & Security. 
2. Tap Turn On Two-Factor Authentication.
3. Tap Continue.

If you're using iOS 10.2 or earlier:

1. Go to Settings > iCloud. 
2. Tap your Apple ID > Password & Security. 
3. Tap Turn On Two-Factor Authentication.
4. Tap Continue.

You might be asked to answer your Apple ID security questions.

You may check the link provided below for more information:

Two-factor authentication for Apple ID

Hope it helps!