The closest Scriptural verse that could support why the Sacrament of Orders cannot be conferred on a woman is 1 Tim. 2:12: "But I suffer not a woman to teach, nor to use authority over the man: but to be in silence."
Plus, is there any biblical precedent for priestesses "according to the order of Melchisedech" (Psalm 109/110:4)?
Here's St. Thomas Aquinas's explanation for why "the female sex is an impediment to receiving Orders:"
Certain things are required in the recipient of a sacrament as being
requisite for the validity of the sacrament, and if such things be
lacking, one can receive neither the sacrament nor the reality of the
sacrament. Other things, however, are required, not for the validity
of the sacrament, but for its lawfulness, as being congruous to the
sacrament; and without these one receives the sacrament, but not the
reality of the sacrament. Accordingly we must say that the male sex is
required for receiving Orders not only in the second, but also in the
first way. Wherefore even though a woman were made the object of all
that is done in conferring Orders, she would not receive Orders, for
since a sacrament is a sign, not only the thing, but the signification
of the thing, is required in all sacramental actions; thus it was
stated above (Question , Article ) that in
Extreme Unction it is necessary to have a sick man, in order to
signify the need of healing. Accordingly, since it is not possible in
the female sex to signify eminence of degree, for a woman is in the
state of subjection, it follows that she cannot receive the sacrament
of Order. Some, however, have asserted that the male sex is necessary
for the lawfulness and not for the validity of the sacrament, because
even in the Decretals (cap. Mulieres dist. 32; cap. Diaconissam, 27,
qu. i) mention is made of deaconesses and priestesses. But deaconess
there denotes a woman who shares in some act of a deacon, namely who
reads the homilies in the Church; and priestess [presbytera] means a
widow, for the word "presbyter" means elder.
Thus, a female cannot receive the Sacrament of Holy Orders just like a priest cannot baptize with motor oil or consecrate a dorito chip.
Every sacrament requires the proper:
- Matter (e.g., unleavened bread for the Eucharist or water for baptism)
- Form (the correct words pronounced to effect the sacrament)
- Intention (to do what the Church does)
If any of these are lacking, the sacrament is not valid.