On many engines, the water pump is driven by the belt as well. If this is the case, it is imperative to have it replaced at the same time. There are two reasons for this, firstly, the water pump is a pulley and bearing that forms part of the circuit the belt travels around and should it fail, then the belt will come off and that is the same as it breaking. Also, water pumps are prone to seizing, which again will break the belt.
The second reason is that should the water pump fail (and not damage the belt etc) and require replacing, then the timing belt would have to be renewed at the same time, so its best to have a new one fitted as a preventative course of maintenance.
Most mechanics will not carry out the work unless the pump is replaced in the situation as they know the consequences!