Hebrews 7:11-14 (ESV)
Now if perfection had been attainable through the Levitical priesthood (for under it the people received the law), what further need would there have been for another priest to arise after the order of Melchizedek, rather than one named after the order of Aaron?  For when there is a change in the priesthood, there is necessarily a change in the law as well.  For the one of whom these things are spoken belonged to another tribe, from which no one has ever served at the altar.  For it is evident that our Lord was descended from Judah, and in connection with that tribe Moses said nothing about priests.
Now, one might wonder where in the Old Testament there is expressed a need for another priest to arise after the order of Melchizedek, rather than one named after the order of Aaron. Of course the writer of Hebrews will get to that in a couple verses when he quotes Psalm 110. The truth though is, that there has been a change. And that change in Priesthood marks a change in the law as well. For if the old law stood, the one that demanded ten percent, abstaining from lobster and shrimp, etc. then the Aaronic priesthood would still be around, and still in play. But these laws have been destroyed, with the arrival of a new priest, who comes not from the tribe of Levi, but that of Judah, and in connection with that tribe Moses said nothing concerning priests.
One wonders then why Mormons make so much about their Aaronic Priesthood. I’ve been trying to stay away from this. But I’m going to go there. Most Mormon’s and I dare say all of them that I know, claim to hold the Aaronic Priesthood. None of them that I know are even Jewish much less of the tribe of Levi, most have some English last name, betraying the upstate New York roots of the religion. It is just a crock to think that you can hold this priesthood if you are not of the tribe of Levi. It was specific to that tribe. The name even implies that Aaron is your ancestor. I mean this is an apostolic succession type doctrine on steroids, it wasn’t enough that one of them laid hands on you, you had to be begotten by a Levite, you have to be the fruit of his seed. You can’t just claim this. And if you do, you are supposed to be living off of tithes, not killing yourself to give them. If you hold this priesthood, then you are bound by the laws that governed it. Which means I ought not see you stuffing your face with pork chops. And when you are at the temple, you should not be “baptizing” dead people, but slaughtering sheep and goats, and burning them on the altar. Oh, and there would only be one temple for you to do that at. God is pretty clear in the Old Testament that there would only be one place where sacrifices were acceptable to him. To be sure that place moved from time to time, but he did not allow for more than one place. Jesus backs that understanding in John 4.