Contradiction with 1 Kings 2:26
This verse, in which Solomon removes Abiathar from being priest, contradicts the inheritance claim because the priesthood should continue in Levi's line, not be removed.
1 Kings 2:26: And unto Abiathar the priest said the king, Get thee to Anathoth, unto thine own fields; for thou [art] worthy of death: but I will not at this time put thee to death, because thou barest the ark of the Lord GOD before David my father, and because thou hast been afflicted in all wherein my father was afflicted. [worthy...: Heb. a man of death]
Contradiction with Hebrews 7:12
This verse, stating that the priesthood has changed, contradicts the permanence of the Levitical priesthood assignment mentioned in 1 Chronicles 6:54.
Hebrews 7:12: For the priesthood being changed, there is made of necessity a change also of the law.
Contradiction with Matthew 12:4
Since this verse discusses David taking the consecrated bread, which was only lawful for priests (Levites) to eat, it implies exceptions to strict Levitical inheritance rules.
Matthew 12:4: How he entered into the house of God, and did eat the shewbread, which was not lawful for him to eat, neither for them which were with him, but only for the priests?