The Levitical Priesthood is Earthly and the Melchizedek Priesthood is Heavenly.
Paul makes clear in the 9th chapter of Hebrews that the Levitical Priesthood was established because of man's earthly and carnal nature. Whereas, the Melchizedek Priesthood is heavenly and is active in eternity. Hence, the Levitical Priesthood becomes inactive even though it's an everlasting priesthood - Numbers 25:12-13.

Believers who are fully Born Again have overcome their carnal inclinations and do not break the Law being subject to its judgements thereby rendering the Levitical Priesthood moot.


The Endtime Kingdom of God
The Kingdom of God that is established at the End of the World will be established under the Melchizedek Priesthood in preparation for Yeshua's return, which will again render the Levitical Priesthood inactive.

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Temple Priesthood Under the Melchizedek Priesthood
Under ancient Israel with the Levitical Priesthood, temple priesthood was administered by the descendants of Aaron. However, under the Melchizedek Priesthood temple priesthood will revert back to the Firstborn.

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Different Terms - Same Concepts
In the New Testament, we see different terms used for the same concepts that we see in the Old Testament

Old Testament	New Testament
12 Tribal Chiefs	12 Apostles High Priest
Seventy Elders	Seventy ​​Luke 10:1 ​High Priest
Prophets	Prophets ​Ephesians 4:11 ​High Priest
Captain/Judges	Pastors ​Ephesians 4:11 ​High Priest
Teachers ​Non-Kohanim Levities	Teachers Melchizedek Priests called as teachers ​Ephesians 4:11

Priests and High Priests
Peter speaking to a congregation of believers states -

"But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light:" 1 Peter 2:9.
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This statement from Peter obviously is referring to all men as a royal priesthood and hence are priests.

​Moreover, High Priests are leaders of congregations.


Why Women don't receive the Priesthood
There seems to be a propensity in modern society to bestow the priesthood onto women. Plainly spoken women are not called or equipped to be proxy saviors. Proxy Saviors are expected to suffer unjustly for others. Fathers and men who God designates as teachers of God's truth also makes them responsible for what they teach hence they are also accountable and answerable to God for the transgressions for those whom they teach.

I would think that women would be glad not to take on this responsibility!