Islam involves a claim of prophecy within our own age of the world i.e. within the past 2500 years or thereabouts. The question nobody seems to want to ask is that of what exactly the words "prophet" and "prophecy" are supposed to mean. Consider...
In Genesis prior to the flood, God speaks to humans directly. The word "prophet" does not occur in Genesis until after the flood and the incident associated with the tower of Babel. In all of Genesis there is just the one vague reference to Abraham as "God's prophet".
After the time of the tower, God no longer speaks to man directly. Between the time of the tower and the time of Zechariah there were a number of INDIRECT means of communication between humans and the spirit world, including prophets, the Greek oracles, familiar spirits (Saul, Samuel, and the "witch of Endor"), and pure electrostatic devices (pyramids, "arc of the covenant" etc.). The "arc of God" or "arc of the covenant" mentioned in the Bible was basically the sort of crude capacitor which Benjamin Franklin would have called a Leydon bottle.
All of those practices involved trance states like hypnosis, all involved static electricity, all involved the use of a part of the human brain which we no longer use, and all of them stopped working prior to the time of Alexander.
Prior to the time of Zechariah, city states around the Med basin had run for centuries on information coming back from those kinds of practices and it worked. But when the surface charge of the planet finally and totally broke down to the point that it could not support that sort of thing any more, the information coming back from such practices turned into mush and it became dangerous to listen to any of them.
Understanding this business requires stitching a story together from several separate and seemingly unrelated pieces of information:
Julian Jaynes' "Origin of Consciousness", which describes the part of the human mind and brain which we no longer use:
The Al DeGrazia/Hugh Crossthwaite works which describe the role of static electricity in ancient religious practices:
http://bearfabrique.org/History/degrazia.html
The descriptions of antediluvian realities from ancient literature, particularly Genesis and Plato's dialogs.
Both Plato and the authors of Genesis describe the antediluvian ability of humans to converse with other animals as if that had been perfectly natural and nothing unusual was required for it. After the flood and the fall of the tower, for some period of time, humans were yet able to converse with animals but something very much out of the ordinary had to happen for it to work. Numbers 22 mentions God "opening the mouth" of the ass in order for her to converse with Balaam and this is precisely the same term we read in ancient literature about priests conducting ritual openings of the mouths of idols to allow people to hear their "voices", as Julian Jaynes describes. This "speech" involved the use of that part of the human brain which we no longer use, again as Jaynes describes.
The question of language evolution: whether things like "Nostratic" or "Proto-World" languages ever actually existed. No theory of language evolution can explain the Indo-European/Semitic divide.
My own take at putting this material together into a coherent story may be seen here:
But, again, somewhere no more than a few centuries prior to the time of Christ, all such practices ceased working.
You've heard/read that "thou shalt not suffer a witch to live". Zechariah 13:3 says that thou shalt not suffer a prophet to live either. Zechariah admonishes parents to simply kill children who go on trying to use their minds that way, claiming that all such people are simply telling lies in the name of the Lord.
The first sentence of the Book of Hebrews amounts to a claim that prophets were a thing of the distant past at the time of Christ:
1 God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets,
2 Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds;....."
Basically, claiming to be a prophet after the time of Zechariah, much less after the time of Christ, is like claiming to be a centaur or a unicorn.
There are other problems with Islam and those are not small or insignificant; but this is the fundamental problem.