I have read about this practice too, in Arabian Sands by Wilfred Thesiger.
It was not “the Arabs” who did this. The Arabian Peninsula is a huge land the size of the United States east of the Mississippi, with several different ecosystems and many different tribes with widely differing cultures. You can’t generalize about “the Arabs” any more than you can about “the American Indians.”
The people who had that practice were certain primitive tribes who lived in the highlands of Hijaz or `Asir in southwest Arabia north of Yemen. An area with a culture quite distinct from that of the rest of Arabia: it was agricultural and not camel-based. They not only removed the skin from the penis and scrotum; they flayed off the skin from the navel to the upper thighs. Yeeesh. The flayed penis was then “kippered” by holding it in the smoke from a fire. It was a rite of passage for adolescents to withstand that much suffering. Of course, a lot of boys died that way, which is why it was never widespread to begin with. This was only done by a few tribes in an out-of-the-way corner of the peninsula along the Red Sea.
The mainstream of Arab culture, the people of Mecca and Yathrib for example, and the long-civilized people of Yemen, practiced the same regular circumcision as the Jews and Americans. Nothing freaky.
The hill-people of Jabal Qara in Dhofar, southern Oman, had a culture that was totally different from the rest of Arabia–for example, they were cattle herders and didn’t use camels. They spoke a different language, and culturally resembled East Africans more than Arabs. Their rite of passage included, in addition to circumcision, flaying a strip of skin off the scalp from front to back, a reverse Mohawk. Then the boy had to run around a circle of women while singing to demonstrate indifference to pain. Their traditional culture was uprooted by the civil war in Dhofar during 1965-1975 and now probably most of them have wound up in urban slums.