The Priesthood is both a gift and a calling and as such, it is the giver of the gift or the caller who decides who to give this gift to or who to call, The Church has declared that Jesus/God has not called women to the priesthood.
Actually no one who has not been called has the right to aspire to the priesthood.
Cf. Num 16
1 Now Korah son of Izhar, son of Kohath the Levite, and the Reubenites Dathan and Abiram sons of Eliab, and On son of Peleth were proud
2 and rebelled against Moses with two hundred and fifty Israelites who were leaders of the community, prominent at the solemn feasts, men of repute.
3 These banded together against Moses and Aaron and said to them, 'You take too much on yourselves! The whole community, all its members, are consecrated, and Yahweh lives among them. Why set yourselves higher than Yahweh’s community?'
4 On hearing this, Moses threw himself on his face.
5 Then he said to Korah and all in his party, ‘Tomorrow morning Yahweh will reveal who is his, who the consecrated man whom he will allow to approach him. The one he allows to approach is the one whom he has chosen.
6 This is what you must do: take the censers of Korah and all in his party,
7 put fire in them and put incense in them before Yahweh tomorrow, and the one whom Yahweh chooses will be the consecrated man. Levites, you take too much on yourselves!’
8 Moses then said to Korah, 'Now listen, you Levites!
9 Is it not enough for you that the God of Israel has singled you out of the community of Israel, and called you to be near him, to serve in Yahweh’s Dwelling and to represent the community by officiating on its behalf?
10 He has called you to be near him, you and all your brother Levites with you, and now you want to be priests as well!
11 For which reason, you and all in your party have banded together against Yahweh himself: for what is Aaron, that you should mutter against him?'
12 Moses then summoned Dathan and Abiram sons of Eliab. They replied, ‘We will not come.
13 Is it not enough for you to have brought us away from a country flowing with milk and honey to kill us in the desert, without your making yourself our absolute ruler?
14 What is more, you have not brought us to a country flowing with milk and honey and you have not given us fields and vineyards for our heritage. Do you think you can hoodwink these people? We will not come.’
15 Moses flew into a rage and said to Yahweh, 'Disregard their cereal offering! I have not taken so much as a donkey from them, nor have I wronged any of them.'
16 Moses said to Korah, 'You and all your party, come before Yahweh tomorrow, you and they, and Aaron too.
17 Each will take his censer, put incense in it, and bring his censer before Yahweh – two hundred and fifty censers. You and Aaron too will each bring his censer.’
18 Each of them took his censer, put fire in it and placed incense on it, and stood at the entrance to the Tent of Meeting with Moses and Aaron.
19 Then, Korah having assembled the whole community to confront them at the entrance to the Tent of Meeting, the glory of Yahweh appeared to the whole community.
20 Yahweh then spoke to Moses and Aaron. He said,
21 'Get away from this community. I am going to destroy them here and now.'
22 They threw themselves on their faces and cried out, ‘O God, God of the spirits that give life to every living thing, will you be angry with the whole community because one man has sinned?’
23 Yahweh then said to Moses,
24 'Speak to the community and say, “Stand well clear of Korah’s tent.” '
25 Moses stood up and went to Dathan and Abiram; the elders of Israel followed him.
26 He spoke to the community and said, ‘Stand away, I tell you, from the tents of these sinners, and touch nothing that belongs to them, for fear that with all their sins you too will be swept away.’
27 So they moved away from Korah’s tent. Dathan and Abiram had come out and were standing at their tent doors, with their wives, their sons and their little ones.
28 Moses said, ‘This is how you will know that Yahweh himself has sent me to perform all these tasks and that I am not doing them of my own accord.
29 If these people die a natural death such as people commonly die, then Yahweh has not sent me.
30 But if Yahweh does something utterly new, if the earth should open its mouth and swallow them and all their belongings, so that they go down alive to Sheol, then you will know that they held Yahweh in contempt.’
31 The moment he finished saying all this, the ground split apart under their feet,
32 the earth opened its mouth and swallowed them, their families, all Korah’s people and all their property.
33 They went down alive to Sheol with all their belongings. The earth closed over them and they disappeared in the middle of the community.
34 At their cries, all the Israelites round them took to their heels, saying, 'We do not want the earth to swallow us too!'
35 Fire then shot out from Yahweh and consumed the two hundred and fifty men offering incense.