I would like to address this issue with one proviso, that being the exclusion of any ceremony that initiates a male into a private or secret society. The intent of this posting, then, is to address the issue in terms of what it is that cultures do to young men to celebrate or initiate the start of what is perceived as manhood. Looked at in this light it seems simple to understand why any society or culture might feel the need for such rites and ceremonies. Put plainly; it is that biology handles this issue for women, men have to do it to one another.
The menstrual cycle announces and, if you like, celebrates the passing of a young girl into the adult phase of her life. Her child bearing years. I know full well that it is entirely possible for a young girl to become pregnant prior to the start of her monthly cycle, but in terms of an excepted societal norm, the beginning of her periods tell the world she has, in fact, become a woman.
In the case of men things are very different. There is no absolute biological moment that announces the becoming of a man from the life of a child. Unless there is war in which a boy can prove his manhood someone has to create an equivalent test or trial for him to pass through in order to prove to the world that he has arrived on the scene. The tribulations that any male passes through in order to prove his manhood are intended to be both advertising to the world, the female population and the "tribe" that his "cycle" has begun and he earned the rights that are usually reserved for the men of the society.
The variations on these trials are as varied as the cultures that create them and yet they all serve exactly the same purpose. They are intend to test the bravery, the spirit and the will of any boy that wants to begin his life in the culture being thought of as a man. The argument can be made that even the U.S. government keeps this tradition alive by having young men at the age of eighteen sign up for Selective Service even in an era that does not have an active draft. By signing up the young man can be said to have proved that he is brave enough, has the will to and spirit to fight if called upon to protect the "tribe".