Contradiction with Hebrews 7:11
It questions the necessity of a new priesthood if perfection were attainable through the Levitical priesthood, which could be seen as indicating the limited or shifting nature of priesthood.
Hebrews 7:11: If therefore perfection were by the Levitical priesthood, (for under it the people received the law,) what further need [was there] that another priest should rise after the order of Melchisedec, and not be called after the order of Aaron?
Contradiction with Hebrews 8:4
Suggests that if Jesus were on earth, he would not be a priest, contradicting the eternal priesthood notion by implying his priesthood is heavenly and not earthly.
Hebrews 8:4: For if he were on earth, he should not be a priest, seeing that there are priests that offer gifts according to the law: [there...: or, they are priests]
Contradiction with Galatians 3:19
Speaks on the law being temporary and added because of transgressions until the seed comes, indirectly questioning the permanence implied in Hebrews 5:6.
Galatians 3:19: Wherefore then [serveth] the law? It was added because of transgressions, till the seed should come to whom the promise was made; [and it was] ordained by angels in the hand of a mediator.
Contradiction with Hebrews 10:11-12
Emphasizes the repeated nature of Levitical sacrifices versus the single, sufficient sacrifice of Christ, highlighting a change in priestly function and permanence of Christ's sacrifice.
Hebrews 10:11-12: And every priest standeth daily ministering and offering oftentimes the same sacrifices, which can never take away sins:
Paradox #1
The potential contradiction or conflict related to Hebrews 5:6 might be tied to the idea of Jesus being a priest in the order of Melchizedek. Historically, Jewish tradition does not emphasize the role of Melchizedek in the same way, which could lead to differing interpretations about the legitimacy or understanding of Jesus' priesthood, as traditional Jewish priesthood comes from the line of Aaron. Christian and Jewish perspectives might thus conflict on this interpretation.