Drawing living things on a whole are frowned upon, and in certain schools of thought considered completely forbidden. Generally, the Prophets as a whole are off-limits (which includes all of the Judeo-Christian prophets), and especially Muhammad.
The reasoning is pretty straightforward. On one hand it is to prevent any prophet or living thing from being deified. On the other, there is an idea of reverence and sacredness.
Depictions of Muhammad are shunned upon to prevent Muslims from revering the Prophet to an extreme where he would have been considered a God, by placing his pictures in home or mosques and praying to him. This is what Muslims believe happened in the case of Jesus, and other cases of god-incarnates in history. If you’ve ever been to a mosque (at least not the new ones built by oil-rich countries), its interiors are actually very minimalist. At most you would see arabian calligraphy and geometrical patterns. God is not a person, but an entity that cannot be realized in human minds.
Islam is very much about strict monotheism, or realizing the truth about the Oneness of God – there is no room for multiple Gods or abstractions of Gods or avatars or incarnations.