Christians state that Jesus was both a King and a Priest. But to a Jew, this doesn't make sense. Did Christianity change the meaning of Priest? What is a King? What is a Priest?
In the Christian bible, Jesus is portrayed as the priest, who is given the priesthood of Melchizedek (as in Psalm 110). One of the important reasons why Jesus is portrayed as a priest is because he is the one who provides atonement via the guilt offering (Leviticus 5:16, 5:18, 6:7; 7:1-6, 9:7).
So Jesus would have had to be a Priest in order to bring a sacrifice according to the law.
It difficult to understate how important this is and how it plays into the Christian theology over Jesus. For now let us just say that everything surrounding Jesus has to fit the letter of the Law in order for Jesus to have fulfilled the law. We are not nitpicking or being picayune at all, this would have been of paramount importance to the Jews Jesus was sent to, and was an issue of deep concern to early gentile Christians as well.
In the Christian bible, Jesus is portrayed as the King; the son of David in order that he may lay claim under the Davidic covenant.
In order to be King, you have to be of the tribe of Judah – “The scepter shall not depart from Judah,” (Genesis 49:10) – and you must be of the house of David, to catch the Davidic Covenant – “…thy throne shall be established for ever.” (2nd Samuel 7:12-16).
In the knowledge of how important and well-known these passages were to every Israelite, Matthew spends a great deal of time (14+ verses) on a genealogy that paints Jesus as being of the house of David in the tribe of Judah.
Emphasizing the Davidic covenant, Jesus also refers to himself as the Son of Man 80 times in the gospels, referencing Daniel 7:13-14. This comes with it's own set of problems, but the message is clear: the New Testament wants Jesus to be seen as King by birthright in the house of David.
Ignoring all problems with Matthew's Genealogy (which are significant), in order to be a priest you have to be the son of someone from the tribe of Levi, and specifically of the house of Aaron ha'Kohein – Aaron the high priest. In short, Jesus was not a “Priest” in the sense required by Christians to satisfy Torah law.
But even if he was – I shouldn't need to tell you that being both of the tribe of Levi and of the tribe of Judah is impossible. It is as impossible as being of the house of David and Aaron simultaneously; one cannot have two fathers. This is decreed explicitly in many places, here are a few passages I was able to pull up off-hand;
7 So shall not the inheritance of the children of Israel remove from tribe to tribe: for every one of the children of Israel shall keep himself to the inheritance of the tribe of his fathers.Numbers 36:7 (KJV)
18 And they assembled all the congregation together on the first day of the second month, and they declared their pedigrees after their families, by the house of their fathers, according to the number of the names, from twenty years old and upward, by their polls.Numbers 1:18 (KJV)
15 Enroll the Levites by ancestral houses and by clans.Numbers 3:15
You cannot be both King and High Priest at the same time. In fact Jewish law contains specific prohibitions against Kings peforming priestly duties and so forth. Famously, the Maccabees broke this rule and were destroyed by God. But in addition there are other kings well known to have committed this sin.
Some other relevant verses;
And thou shalt set the Levites before Aaron, and before his sons, and offer them for a wave-offering unto the Lord. 14 Thus shalt thou separate the Levites from among the children of Israel; and the Levites shall be Mine. 15 And after that shall the Levites go in to do the service of the tent of meeting; and thou shalt cleanse them, and offer them for a wave-offering. 16 For they are wholly given unto Me from among the children of Israel; instead of all that openeth the womb, even the first-born of all the children of Israel, have I taken them unto Me. 17 For all the first-born among the children of Israel are Mine, both man and beast; on the day that I smote all the first-born in the land of Egypt I sanctified them for Myself. 18 And I have taken the Levites instead of all the first-born among the children of Israel. 19 And I have given the Levites–they are given to Aaron and to his sons from among the children of Israel, to do the service of the children of Israel in the tent of meeting, and to make atonement for the children of Israel, that there be no plague among the children of Israel, through the children of Israel coming nigh unto the sanctuary.'Numbers 8:13-19 (JPS)
Numbers 3:5 And the Lord spoke unto Moses, saying: 6 'Bring the tribe of Levi near, and set them before Aaron the priest, that they may minister unto him. 7 And they shall keep his charge, and the charge of the whole congregation before the tent of meeting, to do the service of the tabernacle. 8 And they shall keep all the furniture of the tent of meeting, and the charge of the children of Israel, to do the service of the tabernacle. 9 And thou shalt give the Levites unto Aaron and to his sons; they are wholly given unto him from the children of Israel. 10 And thou shalt appoint Aaron and his sons, that they may keep their priesthood; and the common man that draweth nigh shall be put to death.'Numbers 3:5-10 (JPS)
And Nadab and Abihu died before the Lord, when they offered strange fire before the Lord, in the wilderness of Sinai, and they had no children; and Eleazar and Ithamar ministered in the priest's office in the presence of Aaron their father.Numbers 3:4 (JPS)
8 Then Moses said to Korah, “Hear now, you Levites! 9 Is it too little for you that the God of Israel has separated you from the congregation of Israel, to allow you to approach him in order to perform the duties of the Lord’s tabernacle, and to stand before the congregation and serve them? 10 He has allowed you to approach him, and all your brother Levites with you; yet you seek the priesthood as well! 11 Therefore you and all your company have gathered together against the Lord. What is Aaron that you rail against him?”
31 As soon as he finished speaking all these words, the ground under them was split apart. 32 The earth opened its mouth and swallowed them up, along with their households—everyone who belonged to Korah and all their goods. 33 So they with all that belonged to them went down alive into Sheol; the earth closed over them, and they perished from the midst of the assembly. 34 All Israel around them fled at their outcry, for they said, “The earth will swallow us too!” 35 And fire came out from the Lord and consumed the two hundred fifty men offering the incense. Numbers 16:8-35,
Another interesting thing to note is that being a Priest incurrs sin. If Jesus was a Priest he would have been guaranteed sin, the meaning and punishment of which is not known and may never be known until the end times.
And HaShem said unto Aaron: 'Thou and thy sons and thy fathers' house with thee shall bear the iniquity of the sanctuary; and thou and thy sons with thee shall bear the iniquity of your priesthood.Numbers 1:18 (JPS)
The Christian response is to bring out Hebrews 7, ex. Hebrews 7:8 and/or Hebrews 7:11. The statement will then become that Jesus isn't really the High Priest like a son of Levi, house of Aaron would be High Priest. Instead, Jesus is a priest like Melchizedek.
In other words, the Christian then claims Jesus' priesthood is superior to Aaron's.
Also, at times the Christian may point out that Shem had the role of both Priest and King when he appeared to Abraham. This may or may not be true but it is not relevant, as the institution of King via the Davidic Covenant was not established until much later. It is this covenant which Jesus needs to fufil to be the Messiah – not merely to be a king in a general sense.
Further, Christians will bring Hebrews 7:3 and say that Melchizedek was Jesus, or that he always remained a priest. We know this is not true and the priesthood passed to Abraham. This is shown in Psalms 110 but it is also common sense as there can only be one High Priest at a time anyways. The problem with this is Melchizedek wasn't Jesus, he was Shem – Psalm 110 verifies the Midrash in the same way that Joshua 10:13 and 2 Samuel 1:18 verify the book of Jasher, which is also Midrash i.e. non-canon). Chronicles brings several now-lost books as well, such as Gad and Iddo. Were these books around today, given that Chronicles (supposedly divinely inspired) vouches for these books as containing information overflow from Chronicles, it would be reasonable to accept the information in those books at least in the absence of any other information. Thus there is no reason to assume Melchizedek was ageless, that he didn't have a father, etc.
However, again, none of this really matters because God split the priest-and-king tradition as of Numbers 3:11-13
The response fails because it doesn't make any sense. Melchizedek means “King of Righteousness” – it's a title, not a name. Melchizedek was Shem (according to Midrash). This line of priesthood was transferred to Abraham in Genesis 14 (See Psalms 110). There is no such thing as a separate and superior priesthood. Secondly considering Aaron, God promised that only the sons of Aaron would henceforth hold Priestly office (Numbers 3:11-13). That is, Kohein (which means 'to hold office') and as such would not hold land (inheritance) in Israel. Other kinds of Priest (i.e. Exodus 19:6) have nothing to do with the priestly office nor the priestly duties which God promised solely to the tribe of Levi under Aaron.