What is the justification of disallowing women to become Roman Catholic priests? We all know Jesus had chosen his apostles who are all men. But is there any passage in the bible that says Women cannot become priests?
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 [32], Article [2]) 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.