Well, because Exodus 20:4-6, the Second Commandment, says:
4 “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. 5 You shall not bow down to them or worship them; for I, the Lord your God, am a jealous God, punishing the children for the sin of the parents to the third and fourth generation of those who hate me, 6 but showing love to a thousand generations of those who love me and keep my commandments.
What's interesting is both how lax Christians and Jews are about it, and how severe the wording actually is. By some interpretation, any visual depiction of nearly anything is an idol. Certainly a big statue of Jesus or a fresco of God should both qualify, and yet...
There was a whole schism in the Byzantine Empire during the late 700s over whether religious iconography constituted graven images. This enveloped all the Abrahamic Religions and periodically reasserted itself for nearly a millennium, both in the academic sphere and in riots lead by hot-headed zealots of various sects.
Muslims simply ended up on the iconoclast side of the fence once the dust settled. If you study art history of the region, you get some truly incredibly geometric patterns emerging throughout the Muslim world, well into the 20th century, because of this stricture against iconography. There's some speculations iconoclasm inspired efforts to produce these shapes and patterns, resulting in a heavy religious patronage of Islamic mathematics in much the same way the Renaissance Era in Europe contributed to the modernization of art and sculpture.
But the idea that Islam is somehow unique in the views on artistic reproduction of the human form is really more an artifact of history than of the religion itself. Absent certain twists of fate, we'd be angrily denouncing Muslims for making big bronze statues of their religious figures, which 600 years of Protestant iconoclasty informs us is only something a bunch of evil religious psychos would ever do.
Punish third and fourth generations for the sins of their ancestors. Sure whatever.
Showing love to a thousand who love and keep commandments. Sure fine.
But what happens if my grandparents loved and kept commandments, but my parents didn’t? Does the punishment supersede the love? Or do me and my kids get fucked, but my grandkids are back in the good graces?