Why is BitBay asking for this information when no bank has ever asked me this kind of question?
Banks also verify the source of their customers' funds. They have direct access to the customer's account, and can also exchange customer information with each other, so the process is less "invasive" for the customer, often even unnoticeable.
A cryptocurrency exchange unfortunately does not have this capability, so we are obliged to engage the customer in this process to a much greater extent than other institutions. Banks also occasionally ask customers where the funds in their accounts that are linked to transactions on our exchange come from.