Try not to mix up priesthoods.
Melchezedek priesthood
Aaronic priesthood
Levitical priesthood
Know that ALL of these are OT priesthoods.
That we are all individually and collectively a priesthood, think about that. Why would that be?
I don't think you have any idea what's the difference in the above priesthoods or that we are now part of the priesthood with Christ as the High Priest.
You need to build upon concepts. That's how Christianity is.
So you tell me why these three are different?
What changed that OT priesthoods are no longer valid?
Why is each person part of Christ's royal priesthood now, but not then?
Answer these questions and I'll answer any other questions about this that you have.
You say:
Know that ALL of these are OT priesthoods.
You know that is not true, because Jesus was a priest and an High Priest of the Melchisedec priesthood as recorded in the NT. So it is Jesus himself that bridged the Melchisedec priesthood from the OT to the NT and it is the Melchisedec priesthood that is referred to when Peter tells us we are a "royal priesthood". It is the royal priesthood because it is the priesthood of our Lord, Jesus Christ, he is the great High Priest of our priesthood.
You say: So you tell me why these three are different?
This could be a book, but I will try to condense it to a few paragraphs.
We start with the Melchisedec priesthood. It has been around since Adam and all the patriarchs of the early OT held the MP. In their day and up until Melchisedec, it was known as "The Holy Priesthood after the Order of the Son of God." Melchisedec was a High Priest of god after this order of the priesthood and he was also the king of a region of the country called Salem, (which we think is exactly where Jeru"salem" is located). Because of his extreme righteousness and bringing such righteousness and prosperity to his people, the Lord changed the name of the priesthood to Melchisedec in honor of this great man.
Melchisedec held this priesthood, Abraham received it from him, Isaac rec. it from Abraham, Jacob rec. from Isaac, Joseph rec. from Jacob. Moses had the Melchisedec priesthood, which means that whoever held this priesthood could officiate in all of the high ordinances and govern the church of God as it expanded and grew.
When Moses went to the mountain and obtained the Words of God, the children of Israel revolted against God. God said at that time, he would destroy everyone, but Moses talked him out of that process, and so the Aaronic priesthhod was born. The children of Israel would be governed by a lesser priesthood until they could be taught the righteousness of the greater priesthood. The lesser priesthood came with a lesser law, called the Law of Moses, with myriads of feasts and sabbaths, and signs, and sacrifices, etc. until the children learned slowly about Christ.
Aaron and his sons officiated over the lesser Aaronic priesthood. The Levitical priesthood was set up under the AP to actually do all the work of the sacrifice, to be done by the men of the Tribe of Levi. They set up hundreds of order of priests of the Levitical priesthood
in order that the daily sacrifices could be done. Thousands of oxen and sheep and doves and other animals had to be killed and cleaned and sacrificed and cleaned up, it took thousands of priests to handle this job. That is what the Levitical priesthood did.
So the AP officiated and governed the proceedings of the lesser AP, the LP was set up to assist the High Priest of the AP, and did all the work of the sacrifices etc.
So when Jesus came, all priesthood rights were centered in the AP and the LP, and all rights and power was in these priesthoods. Nobody did anything of a religious, priestly nature without being of the AP or LP.
Jesus was of the tribe of Judah, and not Levi, so why should anyone listen to him? It is because he spoke with authority and because he had the higher priesthood, the MP, which has the right to officiate is all the affairs of God and man.
You say: What changed that OT priesthoods are no longer valid?
When the law of Moses was done away, it did away with the AP and LP and when the new covenant or new law or new testament was set in order by Jesus it necessitated a change in the priesthood. The higher MP was again activated through Jesus Christ and a new day dawned on the world.
You say: Why is each person part of Christ's royal priesthood now, but not then?
The children of Israel showed by their actions (see history in the OT) that they were not worthy to hold the priesthoods.
It was the hope of Jesus that by expanding the MP that all members would step up and literally be priests unto the Lord. An holy nation, a peculiar people, a royal priesthood.
This did not happen, most members were not willing to hold the priesthood and decided eventually that the bishops and elders, and all the other officers could take care of the religious events. So there was a religious class that eventually took over and all the other people were called lay persons, not holding any priesthood, and not wanting to.
And so today, you have the pastors that pretty much do all the teaching and organizing and council and guide etc. But most members let them do most of the work and hold no priesthood. In the Mormon church all worthy men are ordained to the priesthood. Some are valiant and active, some are not. But all can have priesthood authority.