in seems the shulchan aruch holds that it is regarding flatulence
maybe it has to do with particles of feces getting suck to the body (why is flatulence forbidden in tefillin and during prayer)
i never saw that menstruation has to do with clean body
מוחין כו'. מפני שצריכין גוף נקי ונשים אינם זריזות להזהר אבל אם היו חייבים לא היו פטורין מה"ט דהוי רמי אנפשייהו ומזדהרי כנ"ל דלא כע"ת:
where he says that it is because they are not careful to be watchful and that if they would have been obligated to wear them then this (not being careful of flatulence) will not be enough of a reason not to
but woman are anyway not obligated to wear them
Women, slaves, and minors are exempt from reciting Shema and from Tefillin ...
so better that they should not wear them, then maybe passing gas in them
ps (IMO this is since it is good for women not to be tense but relaxed (it is also better for the children))
i heard that their once was a time that even men stopped wearing teffilin since they where lazy from keeping their body clean (from passing gas), but the rabbis were against this.
