Question

You've raised a very interesting question on which there are several opinions. See Jacob Milgrom's commentary on the Jewish Publication Society 5 volume edition of the Five Books of Moses/Torah.

What may have begun as a priestly and/or a royal perogative became, over the course of time, a standard for Jewish men. Today in most liberal congregations - men are expected to wear a tallit and women may have the option or even be expected to wear a tallit. In orthodox congregations only men wear the tallit.