They're asking just to to verify that it's you. They've already pulled up your record and want to make sure that your answer matches what is on their screen. Especially if they have multiple records with the same first and last name.
In Canada, they may typically ask you to provide one or more details like phone number, address, or postal code. I've even heard tellers in a bank ask for info on previous transactions to help verify identity. I've never been asked to provide our SIN number though which is our equivalent to your SSN. That is a bad practice.
If they're using it as the actual account number, I'd cancel all business with them and find another company to work with. Only tax related services like banks and investment companies need the number.