Many don't consider mobile phone two-factor authentication as real two factor authentication. The reason being is that while the phone looks like "something yo

Many don't consider mobile phone two-factor authentication as real two factor authentication. The reason being is that while the phone looks like "something you posess" it is really just an interface for another "something you know" which is your phone account information. As you said, this info can be compromized to intercept or take control of your SMS. Real 2FA uses a token generator device or an app like google authenticator which does the same thing. This is a real "something you possess" as it can't be compromized without getting access to the device.