I am replacing waterpump on 2001 Mazda 626 2.5 v6. It's running off drivebelt. Why would I have to replace timing belt

if the belt is still fine its not necessary to change it, its just safe money if u went to a workshop because he is going to charge u for the water pump and if u do the belt now he cant charge u anything, but later the water pump is fine and the belt not then u are going to pay for the same job.

Depends on how miles you have on the car at this point, if the milage is high and its open have him replace it, it will cost you more in the long run...