I had this exact problem and have retried from time to time during the last 12 months to activate the two-factor authentication in the hope that the message "Two-factor authentication is not available for your Apple ID at this time" would go away sometimes.
Unfortunately that never happened, so I called Apple Support and they gave me the solution! 🙂
I have a Mac with OS X 10.11 El Capitan and an iPhone 5s with iOS 10.2.1.
Here is the solution:
The error message given when attempting to activate the two-factor authentication can be misleading or wrong!
Very often, the problem is that the own Apple ID account setup is not complete and some some important recovery information is missing to Apple. This might be either:
- the primary e-mali address has not yet been verified (go to System Preferences > Account Details > Contact, in order to check and - if necessary - click the "Verify" button next to the e-mail address and complete the process).
- make sure that you have set up your 3 security check questions (see https://support.apple.com/en-us/HT201363 for instructions)
- you must have provided a trusted phone number (in System Preferences > Account Details > Security)
Once all the required information about your Apple ID is complete, the activation of the two-factor authentication should work (that was the case for me: my primary e-mail address was not verified).