Apple has locked 'icolud' of users with one apple device by mandating 'two factor verification'

Why apple has locked 'icolud' users with one apple device by mandating 'two factor verification' that requires two device?

Please note: Not "two step" - "two factor"

OS is Yosemite

I used to have two apple devices and now i sold one and have only one. I have removed the old devices from the "devices" option in my account. Yet to login to my icolud account on my Mac, the two factor verification pops up, without any alternative option such as SMS or call or email. This is bad as i cant use icould functions anymore in my Mac.