The priests had a special place in Israelite society. God instructed that:
21:6 They must be set apart as holy to their God and must never bring shame on the name of God. They must be holy, for they are the ones who present the special gifts to the Lord, gifts of food for their God.
This brought some extra constraints on whom they could marry and whom they could look after in death, and on their behaviour. They also had extra hurdles to qualify for service. Just as any animal sacrifice, the priests had to without blemish. Levites who were born disabled, or who even had a broken arm, could not approach the altar, but they could serve in other ways.
The reason, as always, was that the priests should not bring shame on God’s holy name by their conduct or any other means:
22:32-33 … for I will display my holiness among the people of Israel. I am the Lord who makes you holy. It was I who rescued you from the land of Egypt, that I might be your God. I am the Lord.”