Without father or mother, without genealogy, without beginning of days or end of life, like the Son of God he [Melchizedek] remains a priest forever. (NIV)
1. There are some Trinitarians who teach that Melchizedek was actually Jesus Christ because this verse says he was without Father or mother, beginning or end of life, etc. This cannot be the case, and misses the point of this entire section of Scripture. Knowing the Old Testament, specifically the Law of Moses, and then knowing about the genealogy of Jesus, the Jews did not believe that Jesus could be a high priest. The Law of Moses demanded that priests be descendants of Aaron and of the tribe of Levi. Of course, Jesus Christ came from the tribe of Judah. This “problem” is actually clearly set forth in the book of Hebrews itself: “For it is clear that our Lord descended from Judah, and in regard to that tribe Moses said nothing about priests” (vs. 14).
What is the solution to this problem? This section of Hebrews shows that if Melchizedek can be a priest recognized by the great patriarch Abraham, and he had no priestly genealogy, then Christ can be a priest when he has no priestly genealogy. The Jews were very aware of the “qualifications” for the priesthood, and if someone claimed to be a priest but could not produce the required genealogy, he was disqualified (see Ezra 2:62). Thus, when this verse says Melchizedek had no genealogy or beginning or end, the Jews understood perfectly that it meant he did not come from a line of priests. They never thought, nor would they believe, that he had no father or mother or birth or death. They understood that if Melchizedek could be a priest to Abraham without being a descendant of Aaron, the first priest, then so could Jesus Christ.
2. Jesus Christ cannot be Melchizedek. Hebrews 7:3 says that Melchizedek was without Father or mother and without genealogy (i.e., without one given in Scripture). However, Jesus did have a father, God, and a mother, Mary. He also had a genealogy, in fact, two—one in Matthew and one in Luke. Furthermore, this verse says that Melchizedek was “like the Son of God.” If he was “like” the Son, then he could not “be” the Son of God.
Buzzard, p. 35
Snedeker, p. 464