If you're talking about the leather strap on the front of M1helmets, it just became a popular thing to do. It was the chinstrap for the liner when the liner was worn alone. They wore liners alone more than most people realize, and the liner chinstrap was supposed to help keep the liner on. Helmets were heavy, so when they were in rear areas they often just wore the liner - It offered some protection like a hardhat does. When in the field they did put the liner strap around the front just to get it out of the way, and it did help to keep the liner and shell together. Some just unhooked the liner chinstrap and threw it away. (They were very unpopular, and didn't have much of a purpose - In liners made after 1963, they did away with the liner chinstraps completely)
Many put the helmet strap around the rear of the shell to keep it out of the way.
(Some of it was just beause it was a 'Popular' thing to do - These were mostly kids, and they often did things like others were doing like young people always do)
There was a rumor that passed through the ranks that if there was a nearby explosion and the helmet chinstrap was worn, the concussion would break the wearer's neck, so most didn't wear their chinstraps. (The rumor was just that - a rumor with no truth behind it) - Later they came out with a ball and hook buckle that was supposed to break free if the helmet shell got hit. Partially they did it to get the GI's to wear the chinstrap - the helmet actually offered superior protection if the chinstrap was worn. The little piece to upgrade the buckle could be added to any of the older buckles, and the heavier buckle could also still be worn if the wearer wanted to.
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The anchor stamp came out in the Korean War and was widely used in Vietnam. It was only a manufacturer's logo, and it had nothing to do with the Navy, as some people will tell you. The 'anchor' was only referring to how well the buckle anchored to each other.
The rumor about breaking necks and soldiers wearing the chinstrap on the rear of the helmet seems to be more prevalent in the ETO. In period photos from the Pacific you see more Marines and many have the chinstrap buckled or just dangling when not in combat.