First, I apologize for getting back to you late. Sometimes we have a question slip through the cracks without being addressed.
The Mass that is celebrated every Holy Thursday during Holy Week actually celebrates two sacraments:
- The institution of the Blessed Sacrament or the Eucharist, and
- The Ministerial Priesthood.
Only the feet of men are washed because it was Our Lord's choice that only men could become priests.
When one looks into the nature of the ministerial priesthood, one can understand the logic behind it.
Since Catholic priests take on the person of Christ, in Persona Christi, and really represent the body and words of Christ during the institution of all seven sacraments, only men can be priests, seeing Jesus Himself was "The Man", as St. Paul said. (1 Timothy 2:5)
You can find more in our searchable knowledge base:
There are a lot of quick answers there, so give it a try. Just search on words of interest like this:
I've also grouped the type of questions into similar faith categories here:
Pope St. John Paul II also wrote an encyclical on this:
In my opinion, many pastors unintentionally downplay the institution of the priesthood on Holy Thursday because they instead focus on the Universal priesthood, that we all share via our Christian Baptism.
Because the emphasis is on the universal priesthood and not the ministerial priesthood, these parishes usually wash the feet of both men and women and thus downplay the ministerial priesthood — not good for young Catholic men who may have a calling to the Catholic priesthood.
I searched the knowledge base for you and found these web postings that should answer, if not help answer, your question. If you go a bit down this first posting, you will see what Pope St. John Paul II said on this in his 1995 Letter to Priests on Holy Thursday. (Note Section 7.)
Again, sorry for the late response.