itīs standard for every airline I know that a child under 2 is considered an infant and does not have itīs own seat, however I fully agree that AB should have the flexibility to book an additional seat if you wish to and also offered to pay for it.
I suggest to try call again and hope for a more capable agent. While I have no experience in booking an additional seat this should be a process which is typically offered by airlines also in other cases, such as transporting your cello.