Contradiction with Numbers 25:13
This verse speaks to a perpetual priesthood for Aaron's line, which contrasts with the idea of a new, unchangeable priesthood in Hebrews.
Numbers 25:13: And he shall have it, and his seed after him, [even] the covenant of an everlasting priesthood; because he was zealous for his God, and made an atonement for the children of Israel.
Contradiction with Psalm 110:4
While it confirms the priest forever aspect in Hebrews 7:21, it could be seen as contradicting by showing that the order of Melchizedek means a different kind of priesthood than the Levitical one.
Psalm 110:4: The LORD hath sworn, and will not repent, Thou [art] a priest for ever after the order of Melchizedek.
Contradiction with Hebrews 7:12
This verse indicates a change in the law with a change in priesthood, which may appear to contradict the oath-bound permanence described in Hebrews 7:21.
Hebrews 7:12: For the priesthood being changed, there is made of necessity a change also of the law.
Contradiction with Exodus 40:15
Establishes Levitical priesthood as everlasting, seemingly contradicting the notion of a new, everlasting priesthood like in Hebrews 7:21.
Exodus 40:15: And thou shalt anoint them, as thou didst anoint their father, that they may minister unto me in the priest's office: for their anointing shall surely be an everlasting priesthood throughout their generations.
Contradiction with Leviticus 6:22
Specifies the ongoing requirement for Aaronide priesthood, in contrast to the priesthood of Jesus implied in Hebrews 7:21.
Leviticus 6:22: And the priest of his sons that is anointed in his stead shall offer it: [it is] a statute for ever unto the LORD; it shall be wholly burnt.