Short answer
Most Muslim scholars hold that pictures of the Prophets ﷺ should not be made, to protect people from sliding into idol worship and to keep respect. It is not that Muslims are against art: Islamic calligraphy and geometric design are great traditions.
The fuller answer
Islam's main concern is the worship of God alone. Pre-Islamic Arabia was full of idols, and the Prophet ﷺ removed all of them from the Kaaba. To prevent images of him from ever becoming objects of devotion, and because nobody can accurately portray him, Muslims do not depict him, and many do not depict any prophet.
This is why Muslims are offended when he is mocked in cartoons. It does not justify violence: the Prophet ﷺ himself was insulted and responded with patience, and Muslim scholars condemn attacks on people because of insults. The right response is peaceful protest, dialogue or ignoring it.
This answer follows the mainstream Sunni understanding and is general learning, not a fatwa. Where Muslims differ, the answer says so. Have a question of your own? Write to us.