>>It was explained, fairly nicely, how SMS is better here. If you don't agree you have to address that, not just say that two factor auth is a red herring.
Fair enough. The false dilemma is more easily seen if the argument is stated like this:
"We cannot guarantee the safety of your data unless you give us your phone number"
"We cannot be certain of your identity unless you give us your phone number"
Are either of those statements true? Of course not!! I'm not making an argument against security. Hooray for security already. I'm just saying that your phone number is not a requirement for your data to be secure or your identity to be confirmed.