Do we know why Jesus Christ, the Second Person of the Trinity, is male? Until we do, we won't know definitively why women cannot be priests ---- or know definitively why they should.
Jesus the Second Person is the first person ever to possess this faculty called 'priesthood'. He is the prototype. No priests existed before him because nobody existed before him. There is no way for a human being to assess from his or her own knowledge or reasoning whether the faculty called 'priesthood' is separable from Jesus' other features such as his looks, height, intelligence, colour of hair, etc. We might hazard a guess that it is, that Jesus' priesthood does not depend upon the colour of his hair, but it is only guesswork. We cannot for certain say that Jesus' priesthood is or is not connected to the colour of his hair because we had never known of this idea of p-r-i-e-s-t until he came along. Before him, there were no priests. When he came along, he came as a parcel of features, just as we all do, and we could not diivide him into strands and say that this strand is important for priesthood but that isn't. There was simply no precedent for knowing what about him was necessary for being a priest and what wasn't.
What about Hindu 'priests' and Mayan 'priests' and priests from older cultures perhaps than those of the Jews? We attribute to them the function of 'priest' as a borrowed word. We say they are 'priests' because they do sacrificial stuff sort of like the stuff we have seen the Jewish priests to do. But this is an anachronistic or retrospective application of the word. The Jewish priests did what they did - bloody animal (but not human, as did 'priests' from other cultures) sacrifice - as a precursor to the bloody sacrificing of the Messiah - because they were inspired by the Spirit of God under the command of God the Father through the Second Person of the Trinity to do so, everything that God the Father does being done for and through his Son. We call the Hindu and Mayan guys doing sacrificial-type stuff 'priests' because what they do is vaguely similar to what Jewish priests did and we have no other word in our vocabulary to use. We are comparing them to a faculty derived from our knowledge of Jesus, even though, humanly speaking, he didn't turn up until long after the Hindu and Mayan guys had been strutting their stuff, so to speak.
So how do we now know that looks, height, intelligence, colour of hair, place of birth, occupation and most other human characteristics have nothing to do with the faculty of priesthood? By watching Jesus choose as his future first priests men who were not born in Bethlehem, did not grow up in Nazareth, did not receive the religious training that would entitle them to be called 'rabbuni', were not carpenters and, we can reasonably surmise, looked and weighed and had skin tones that were different from his. He established by his choice, confirmed by the Holy Spirit at Pentecost, that those features were irrelevant. He never said that those features were irrelevant but his conduct says it for him. But, somehow, he never chose a woman to be an apostle, and, looking at what he did from afar, we surmise that his conduct is telling us that the human feature of gender is relevant to priesthood.
Jesus only chose Jewish men to be his first priests. He himself, the prototype, was Jewish. Today we have men from all races being ordained as priests. Can non-Jews be ordained? Samaritans could become followers of The Way but could they be chosen by the laying of hands to become the next generation of apostles? I don't know whether records kept by the early church that didn't make it into the canon contained evidence of Samaritans being chosen as successors to the apostles but there is scriptural evidence of men of mixed parentage closely associated with the work of spreading the gospel, and so we have confirmation that race is irrelevant to priesthood.
Over the course of time, various human characteristics have been peeled away by the Church, as the teaching successor to Jesus the Word, as irrelevant to eligibility for priesthood. You can even once have been an accessory after the fact to murder, like St Paul when he was the pharisee Saul of Tarsus. He was picked personally by Jesus. Reformed acessories to murder? No problem. But women? No evidence, at a time when there were always women travelling with and supporting Jesus' travelling band, when there were Marthas who were intensely interested in learning the faith and Veronicas willing to identify themselves publicly with what seemed to be the lost cause of a silly crank, that they were rewarded for their faithfulness by being commissioned to apostolic leadership.
And so the matter rests. When we know why Jesus the Second Person was always a male, God being perfect because there is no shadow of change in him, the body that he took into Heaven always being the body suit he will be wearing and was the body suit he was wearing before anything was created, we'll know why women cannot be priests. And because God is the unity of the empirical and the normative, the unity of what is with what ought to be, and the sole standard of morality in the universe, Jesus is male because he ought to be male and ought always to have been male and because it would be immoral if he were not male. Stacked up against this faith-based reality, it's not surprising that the Church does not consider itself free to ordain women as a functioning female Jesus. That would be committing a blasphemy.