“It is part of the uniform of a Yeshiva man. It indicates one is a member of the Yeshiva community much the same way fatigues uniform indicates one is a member of the military”
Not all branches of the military wear fatigues. Naval personnel for example do not, yet are members of the miliiary. Similarly, one may wear a black hat, yellow hat, purple hat or no hat at all and still be a member of the group known as “yeshiva men”.