Why is it bad to cut down trees that animals are living in?

Maybe it's bad to cut down trees animals are living in for the same reason that you might consider it bad if someone came along and bulldozed your home for no reason you could understand. It'd be even worse if you were in your home at the time.

In some places there are laws which say if a species of animal which is under legal protection is living in an area which must be cleared or damaged in some way as to make it uninhabitable to those animals, consideration has to be given to whether there's an alternative to clearing that area, and, if no alternative can be found, the animals must be relocated to a suitable alternate area with as little disturbance as possible.