It may have something to do with the fact that he is essentially under-occupying the property, being a single person in a 3 bed house.
The reason for refusing an exchange, which they can do in most circumstances are:
1. They want to be able to offer the property to those requiring housing in their own borough if the single tenant moves out.
2. They may be looking to start an under-occupancy action against the tenant but have not started. But most LA's dont normally carry this out as it there can be many legal complications.
My advise to the guy with the 3 bed house is to seek legal advise and get the LA to define why they wont allow the exchange to take place!