This is all taken from the following page..I copied most of it to paste..there may have been a few more points in there I left out here if you'd like to check it out:)..There are also some other links on the page so visit it.This is for trinitarians who can't do their own research ;)..
Hebrews 7:3: without father or mother, without lineage, having neither beginning of days nor end of life, but resembling the Son of God, he remains a priest in perpetuity. (Montgomery)
Some, in reading the above scripture, see something in it that is not there, that Jesus has neither beginning of days, nor end of life. They do not seem to notice that when saying that *he* has neither beginning of days, Paul is speaking, not of Jesus, but of Melchizedek (also spelled Melchizedec), and not literally, but figuratively, to show the difference between the priesthood of Jesus and the Aaronic priesthood. If one reads this literally then we must believe that Mechizedek was always a priest from eterity past and that he is still now a priest. Jesus, of course, did begin his priesthood, but not with a lineage or beginning of days here on earth, but in heaven. There is no earthly lineage, no earthly beginning, from which his priesthood is attached. There is nothing here that says that Jesus existed for eternity past; such has to be read into the text.
Paul says that Melchizedek resembles the Son of God. Yes, Jesus is Son of God [He is not the God of whom is Son], and yes, Jesus does live forever, having been given such power by God, although this is not what is being spoken of in the verse, for it is concerning the priesthood that Paul is speaking, not existence. Paul is not saying that Jesus exists “from eternity”; this has to be imagined, assumed, and read into what he said. The only reason I can see for reading this into the text is to promote the idea that Jesus is Yahweh.
Very few believe that Melchizedek is God Almighty himself, having lived for eternity past, having no beginning, no ending, etc. Very few believe that Melchizedek literally continues to be a priest even to this day and forever. And, of course, we know that Jesus had a father. But Jesus had no earthly father from which he obtained a priesthood. To take the view that Paul is speaking literally would make Melchizedek Yahweh, and not our Lord Jesus, who is called the “only-begotten” (John 1:14,18; 3:16,18; Hebrews 11:17; 1 John 4:9), “the Son of God” (Mark 1:1; Luke 1:32,35; John 1:34; 3:18; 5:25; 6:27; 9:35; 10:36; 11:4; 20:31; Acts 9:20, etc.), “the beginning of the creation of God.” (Revelation 3:14)
It would scarcely be necessary to show that Christ was not without a Father. Call to mind his words: “Father forgive them;” (Luke 23:34) Jesus was “born of a woman.” Wakefield’s version renders this (Hebrews 7:3) “Of whose father, mother, pedigree, birth, and death, we have no account.” There was a strict record kept of parentage, birth, death, &c., of every Levite, so that any one claiming to be a priest or Levite could prove it by the records.
It is testified of Melchizedek that he had no end of years, yet we do not see him living today; and it is testified of Christ that he did die, but he was made alive. This same Paul could say of Christ: “Jesus Christ, by the grace of God, tasted death for every man.” We conclude, then, that as Christ, in the days of his flesh, had a Father existing on the spiritual plane, and a mother who existed on the earthly plane. Jesus did “die for our sins,” “even the death of the cross,” therefore we have to conclude that Paul is not speaking literally about either the lack of father, birth or death of either Melchizedek or Jesus in a literal sense, but rather he is illustrating the lack of genealogy of the order of the Christ’s priesthood as shown by the account of Melchizedek, and thus Jesus’ priesthood is after the order of Mechizedek, not being of Aaronic genealogy, not having any earthly beginning or end.
When is Jesus made priest after the order of Melchizedek? Has he always been such a priest? No, but while this priesthood has no earthly beginning — he could not even have been such a priest while on earth, while in the days of his flesh, nor did Jesus have an earthly father from whom he could claim a priesthood — he was made priest after his return to heaven. (Hebrews 8:1-4; 9:11; 10:11-12) Thus like Melchizedek, Jesus’ priesthood does have a beginning in the heavens, but it is not seen on earth, nor is it given as a result of any earthly inheritance of the law and its priesthood. Like Mechizedek, Jesus does not literally have “no beginning of days”, but his heavenly priesthood has no beginning of days on earth, nor can be it be accounted for by human descent.
Jesus, now possessing endless life that will never die again, and he will be a priest for all eternity. — Romans 6:9; Hebrews 7:8,16,24,25; Revelation 1:18.
To interject a meaning into Hebrews 7:3 that Jesus is God Almighty because of the description given to Melchizedek is to derive such a meaning out of context, and detract from what Paul was actually saying.
Nor did Jesus glorify himself as priest, for we read: “Christ did not glorify Himself to become High Priest.” (Hebrews 5:5) It is Yahweh himself that speaks to the Messiah saying: “You are a priest forever according the order (manner, Hebrew Dibrah, Strong’s Hebrew #1700) of Melchizedek.” (Psalm 110:4) Thus Paul says that Jesus is “named by God a high priest after the order (fashion, Greek, Taxis, Strong’s Greek #5010) of Melchizedek.” (Hebrews 5:6,10; 6:20; 7:11,17,21) And it is Yahweh, the God and Father of Jesus, who speaks to the Messiah, saying: “Sit at my right hand until I make your enemies your footstool.” — Psalm 110:1
Thus there is nothing in Hebrews 7:3 that proves that Jesus is Yahweh.
Even as Jesus is made a perpetual priest, Melchizedek is made by Yahweh in the prophecy of Psalm 110:4 (Hebrews 5:6,10; 6:20; 7:11,15.21) like the Son of God pertaining to the priesthood of the Son of God. So that Jesus becomes a priest after the likeness of Melchizedek. (Hebrews 7:15,21) It does not prove anything, however, about the definition that trinitarians would like to give to eternity (as having no beginning), for Jesus has not always been a priest.
The fact that Melchizedek is made like the Son of God does not do away with the fact that it is of Melchizedek that Paul says that he is without beginning of days and or end of life.
There is no genealogical record of Melchizedek, his priesthood had no genealogical record of its beginning of days and no record of its ending of life. Paul is, of course, speaking symbolically, and not literally. Nevertheless, this is how his priesthood is a type of the priesthood of Jesus. We know that Melchizedek’s priesthood actually did have a beginning, and we know that Melchizedek himself did have a beginning, even though we do not know who his father and mother were, nor when he was born, when his priesthood began, etc. Nevertheless, his priesthood was not one that had a heritage from a lineage of priests, and in this Melchizedek is like Jesus. This is Paul’s argument in Hebrews chapters 3 through 10. “After the likeness of Melchizedek there arises another priest” (Hebrews 7:15), a priesthood superior to that of the Aaronic priesthood; Jesus did not receive a lineage as a priest from Aaron. Thus Melchizedek — is made, rendered similar, by the expression of Yahweh (Psalm 110:4), to the priesthood of Jesus. We also know that Jesus was not such a priest while on earth — thus he did not become a priest after the order of Melchizedek until after he was raised from the dead. He did become a perpetual priest after his ascension.