Hey,
You must have brought this fact directly to the officials of Emirate flight rather than talking to the travel agent. They have already mentioned in there site
http://www.qwiknumbers.com/emirates-contact-number on this subject which I am enumerating below:-
"You can change your destination or origin,or add and remove stopovers, or change the dates and timings of your flight.All these changes can be made through the ‘change my booking’ link in Manage a Booking.If you cannot see the ‘change my booking’ link, please contact your local Emirates Office.There may be a fee associated with making changes to your booking depending on the fare conditions of your ticket."
Two months back when I booked my seat for Switzerland, my program was cancelled and I want to extend the date of my visit , I called Emirates Airline customer service and they forwarded my call to the concerned department and after hearing me, they solved my problem.