Maybe using the word upgrade was the confusing thing. Emirates does offer paid upgrades on some routes which is perhaps what they thought you were talking about.

Perhaps call back and just say that you want to make a change to a booking and then when they have the booking details, tell them that you want to change it to be booked in business class.

Just avoid the use of the word "upgrade" mayhaps

If the flight is fully booked in the revenue business classes, then it will not matter of course.