Melchizedek, whose name literally means king of peace and righteousness, was a distinct kind of priest who directs our attention to the perfect, unique priesthood of Jesus Christ. The position of High Priest is exclusively reserved for Christ. His priesthood, which is of Melchizedek's priestly descent, is superior to the Levitical priesthood because it is eternal (Hebrews 7:11-12; 23-25). Jesus Christ forever lives to make intercession for those who approach Him. This source provides the following commentary on the meaning of the word "unchangeable" as rendered in Hebrews 7:24:
"The key word is “unchangeable” (aparabatos), which suggests that the Lord’s priesthood is imperishable. Some suggest that the meaning of the Greek term is simply “permanent, unchangeable” (F.W. Danker, et al., A Greek-English Lexicon of the New Testament, Chicago: University of Chicago, 2000, p. 97), which, of itself, would eliminate the Mormon idea. But even more to the point is the proposed meaning “non-transferable” (C. Spiqu, Theological Lexicon of the New Testament, Peabody, MA: Hendrickson, 1994, 1.143-44). That would specifically deny that it could pass to other persons."
Thus, the Mormon church's claim to possessing a priesthood after the order of Melchizedek has been fabricated out of thin air. It has not been sanctioned by God. In other words, men have arrogated for themselves a position that only Christ can take on. The Bible nowhere makes mention of a distinguished hierarchy of priests who preside in accordance with Melchizedek. In fact, this ruling male figure is mentioned only twice in the Old Testament as he blessed Abraham (Genesis 14) and in a Messianic Psalm (Psalm 110).
Furthermore, the assertion that Mormons have been conferred with an Aaronic priesthood is refuted because that ministerial office has been fulfilled by the Cross. Jesus Christ is the only way in which man in his sinful condition can come near to God. The tearing of the veil in the temple signifies the termination of the Lord dwelling in tabernacles made with human hands (Matthew 27:51-54). The type of priesthood set forth by the New Testament is the priesthood of all believers (1 Peter 2:5-9; Revelation 1:5-6).
The priesthood that was operative during the Old Testament was kept specially for Aaron and offspring within the tribe of Levi (Numbers 3:6). That would disqualify the Mormon priesthood because it contains Gentiles. The Mormon priesthood also does not offer blood sacrifices and follow various temple ceremonies as prescribed by the Law. And lastly, this article excerpt is noteworthy here:
"Researchers who have closely examined the D&C and primary source accounts found that the official narrative of priesthood restoration contains numerous gaps, inconsistencies, and contradictions. Scholars also raise important questions that expose potential weaknesses in Smith and Cowdery's story of their miraculous ordinations. For example, if Joseph and Oliver had experienced events as remarkable and life-altering as divine visitations by John the Baptist and three of Christ's apostles, why would they not tell others? These miraculous ordinations were not publicly revealed or documented until five years after they supposedly occurred. Moreover, if the restoration of the priesthood is a fundamental tenet of the LDS Church, why was this revelation excluded from the Book of Commandments when it was originally published in 1833, only revealed in the revised and re-named Doctrine and Covenants in 1835?"