The Bible does not say why Michael and Satan were arguing over the body of Moses.

It is possible that Satan wanted to use the body of Moses to get the Israelites to fall into idolatry. Seven hundred years after it was made by Moses at the commandment of God, (Numbers 21:8-9) the Israelites were worshipping the bronze serpent and offering incense to it (II Kings 18:4). It is not too much of a stretch to believe that they would soon worship the body of Moses if it were enshrined somewhere.