Why would statues be destroyed in the name of religion?

The answer to this question really depends on who is doing the destroying.

Generally speaking, the three main monotheistic religions (Judaism, Christianity and Islam) have an aversion to "idolatry" - worshiping physical images. This comes from the second of the ten commandments:

"You shall not make for yourself an image in the form of anything in heaven above or on the earth beneath or in the waters below.You shall not bow down to them or worship them"

Exodus 20:4 (NIV)

In order to protect members of their society from breaking the commandment, and to remove from their culture objects which they believe to be offensive to God, zealous followers of their faith have destroyed statues and shrines throughout history.

Destroying an opposing religion's statues and temples was also a brutal way of imposing your belief system on a society. Rather than promote the virtues of your own faith, you destroy the focus and foundation of your opponent's religion. In times where religion was a political force, imposing a belief system on "conquered" territory was important as following another faith effectively treason.