Now waht is the reason for the Bar Mitzvah in the first place?
a) For the family to show off its wealth, social standing and frumkeit? From some of Rav Moshe’s writings brought down in this this thread it appears that here in the USA that has become a reality in too many cases.
Lets try to be more positive:
b) To inaugurate the boy into active participation in Tefilah B’Tzibur. He can now read the Torah, lead services and count towards the quorum of 10 needed. This is like a regular Kohain on his first day of Avodah in the Beit HaMikdash.
With b) Bar but not Bat Mitzvahs would be advisable.
However the term Bar Mitzvah implies what Philosopher above stated: “starts having a chiuv to perform the mitzvos”. Which becomes c).
My initial post was based on either a) or b) being the case.
However, the term Bar Mitzvah implies much more than one group of Mitzvos no matter how important they are.
Based upon c) Bat or Bas Mitzvas should also be done.