In the series “12 reasons why Melchizedek was actually the pre-incarnate Word of God” the following article is reason # 3.
Melchizedek has no mother nor father nor descendants.
Without father, without mother, without descent, having neither beginning of days, nor end of life; but made like unto the Son of God; abideth a priest continually.
– Hebrews 7:3
The writer of Hebrews 7:3 tells us that Melchizedek did not have any parents nor descendants. In other words, God is revealing to the reader new information about Melchizedek that was previously unknown in Genesis 14. Yet, some Bible commentaries wrongly confuse this verse to mean the opposite of what the writer actually says. These Bible commentators would have us believe that Melchizedek’s genealogy is simply missing from the Genesis 14 narrative. If these commentators are right, this would mean that Hebrews 7:3 is not really divine revelation but rather an unnecessary inference from the silence of Scripture. After all, if it is necessary to infer that every named person in Scripture who lacks an included genealogy is parentless, childless and immortal then it follows that the nine kings of Genesis 14:1-2 are all parentless, childless and immortal. Moreover, if it turns out that the writer of Hebrews is given to this sort of faulty reasoning, not only does this undermine the entire corpus of Scripture, it also introduces an appalling hermeneutic that is clearly unsustainable.
However, I believe that the writer of Hebrews means exactly what he says.
Scripture calls angels the “sons of God” (Job 38:7) even though (or rather because) they were directly created by God. The fact that angels neither procreate nor have any angelic parents helps them to meet all the “Without father, without mother, without descent” criteria regarding Melchizedek. However, Hebrews 7:3b also says that Melchizedek is uncreated (i.e. without beginning of days) therefore Melchizedek could not be a mere angel. While Adam and Eve also had no parents they did have descendants so they are also disqualified. All other created men are the product of parents so no mere man could be said to match the description given in this excerpt as well. In light of these facts and the other things mentioned about Melchizedek, it is only right to conclude that Melchizedek must have been the pre-incarnate Christ, yet many Bible commentaries sacrilegiously suggest that the writer of Hebrews is mistaken about Melchizedek’s lack of genealogy.
For example, regarding Hebrews 7:3 and the phrase “without father, without mother, without descent” The Preacher’s Complete Homiletical Commentary states:
These are not stated as actual facts concerning Melchizedek. They are true so far as the narrative of Genesis presents him to us. He is set before us without any genealogy. The writer argues from the silence of Scripture.
Matthew Henry states:
Melchizedek is spoken of as a king of Salem, supposed to be the place afterwards called Jerusalem, and it is generally thought that he was only a man. The words of the apostle, Hebrews 7:3, state only, that the sacred history has said nothing of his ancestors. The silence of the Scriptures on this, is to raise our thoughts to Him, whose generation cannot be declared.
This must not be understood according to the letter; but the scripture has chosen to set him [Melchizedek] forth as an extraordinary person, without giving us his genealogy, that he might be a fitter type of Christ, who as man was without father, as God without mother; whose priesthood is without descent, did not descend to him from another, nor from him to another, but is personal and perpetual.
Our writer refers here not to historical facts about Melchizedek but to what Scripture fails to record about him, employing an argument from silence which, Bruce notes, played “an important part in rabbinical interpretation of scripture.” 
This is rabbinical hermeneutics (midrash) based on the fact that Melchizedek’s lineage is not given in Gen_14:18-20. Like all human beings Melchizedek had parents, but he serves as another type of the eternal Messiah [Utley Heb 7:3]
Without father and mother he was not in respect of generation, but in respect of commemoration; his parents are not mentioned: no more are Job’s, or the three children’s. [Trapp H7:3]
The meaning is that there is no record concerning his parentage. (VWS Heb 7:3)
The argument is that from silence, made much of by Philo, but not to be pressed. The record in Genesis tells nothing of any genealogy. Melchizedek stands alone. He is not to be understood as a miraculous being without birth or death. Melchizedek has been made more mysterious than he is by reading into this interpretation what is not there. [RWP H7:3]
When nothing is recorded of the parentage of this man, it is not necessarily to be assumed that he had no parents but simply that the absence of the record is significant…It is when the writer bases his exposition on the silence of Scripture that his method of exegesis seems strangest to modern readers. [Constable]
Dr. Arnold Fructenbaum’s Ariel Ministries states:
Melchizedek was simply a human being who happened to be both the king and priest of the city of Jerusalem in the days of Abraham. The point of Hebrews is not that he did not have a father and mother, but only that there was no record of it. [19A]
So as one can see from all these comments, irresponsibility with the words of God apparently know no limits in regard to the eisegesis of men who apparently harbor a low view of Scripture. There are many problematic conclusions that arise with the above quotes but time only permits us to examine a few. If we allow the comments written by these theologians to stand then we are forced to conclude that:
1. The writer of Hebrews is a terrible logician
This is because in logic (which is the science of necessary inference) one commits the fallacy of asserting the consequent to argue that:
If an individual suddenly appears in the biblical record for a brief verse or two and no genealogical information about the person is provided, then this must mean that such a person is parent-less, without descent and immortal.
Such a conclusion is fallacious because it is an unnecessary inference. There are any number of other reasons that could equally explain why Melchizedek’s genealogical information is omitted or why he is only mentioned briefly in the Torah. Perhaps his genealogy is not pertinent to the Genesis 14 narrative or perhaps the author simply did not want to include it. Certainly it can’t be said that the biblical author is setting a precedent by not including Melchizedek’s genealogical information at this point in the Scriptures since 17 verses prior to introducing Melchizedek, Genesis 14:1-2 lists nine other kings without providing the genealogy of any one of them. Therefore, if the commentaries above are right about the claim that the writer of Hebrews is “employing an argument from silence” then what follows is that such a person is an irrational thinker. Yet, not even one of these commentaries think to either accuse the writer of Hebrews of being irrational or the Hebrews account of being uninspired. Fortunately, God is the ultimate Author of Hebrews and God is not irrational but is the standard of rationality so we can neatly dispose of any notion that Hebrews 7:3 is based upon “an argument from silence.”
2. The book of Hebrews contains an unsustainable hermeneutic
The writer of Hebrews is said to employ a hermeneutic that allows for barely mentioned persons in the Bible to be deemed parent-less, immortal and without descent. This hermeneutic is not at all impugned by theologians who dispute Melchizedek’s divinity so based upon their silence anyone should be allowed to apply this hermeneutic to other parts of Scripture containing individuals that meet the same criteria. For instance, in Mark 15:43 we are introduced to Joseph of Arimathea who is mentioned only one other time (John 19:38) in the Bible. Based upon the hermeneutic that was allegedly used in Hebrews 7:3, one could similarly conclude that Joseph of Arimathaea was parent-less, without beginning or end, and without descent. Yet, it’s expected that not even the staunchest of these compromising theologians would accept this conclusion. Therefore any dissent to one describing Joseph of Arimathea as parent-less and immortal demonstrates that the hermeneutic allowed in Hebrews 7:3 is unsustainable elsewhere.
So we can clearly see that Scripture is revealing knowledge from the Holy Spirit and not irrationally presenting arguments that are solely based upon the silence of things not mentioned in Genesis 14 as cited excerpts from dissenting theologians would have us to believe.
15. See notes on Hebrews 7:1-3, THE PREACHER’S COMPLETE HOMILETICAL COMMENTARY, Rev. George Barlow and Rev. Robert Tuck, EDITED BY JOSEPH EXELL
16. See notes on Genesis 14:17-20, Matthew Henry’s Concise Commentary on the Whole Bible, Dr. Matthew Henry
17. See notes on Hebrews 7:1-10, Matthew Henry’s Commentary on the Whole Bible, Dr. Matthew Henry
18. See HEBREWS 7, E. MELCHIZEDEK LIKE THE SON OF GOD (7:1-3), THE COLLEGE PRESS NIV COMMENTARY NEW TESTAMENT, DAVID A. FIENSY, Ph.D., Jack Cottrell, Ph.D., Tony Ash, Ph.D.
19. See notes on Hebrews 7:1-3, Bible Lessons International, Dr. Bob Utley
See notes on Hebrews 7:3, The Expository Notes of Dr. Constable (Dr. Constable’s Bible Study Notes), Dr. Thomas L. Constable