Two reasons that Jesus commanded the leper to show himself to the priest and offer a gift:
Jesus wanted the leper to follow the law (Leviticus 14:1–32): to show his healing to the priest and bring an offering of thanksgiving to God (Leviticus 14:4, Leviticus 14:10, Leviticus 14:21). The priest’s inspection would verify a sign of the coming of the kingdom in the healing of a leper (see Matthew 11:5).
Jesus puts the leper’s following of the law of Moses (Leviticus 14:1–57) as the priority.
Interpretation 1:
Upon being healed, the leper had to go show himself to the priest for inspection and bring a gift offering in accordance with the statutes of Moses (Leviticus 14:1). Instead of proclaiming the miracle of his healing far and wide, he had to go straight to the priest to show himself to be healed and to bring an offering of thanksgiving to God as the law demands (Leviticus 14:4, Leviticus 14:10, Leviticus 14:21). This inspection would serve as a witness not only to the priest himself but to the people as a whole that the Messiah has appeared, for the healing of lepers served as a sign of the arrival of the Kingdom of God (Matthew 11:5).1
Interpretation 2:
The fact that Jesus commands the cleansed leper not to say anything about his cleansing for now, but to show himself to the priest and to bring the sacrifice instituted by Moses (Leviticus 14:1–57), testifies to the fact that Jesus keeps the law of Moses.2
3 Jésus étendit la main, le toucha, et dit: Je le veux, sois pur. Aussitôt il fut purifié de sa lèpre.