The argument is, that as such meals were appointed in honor of Yahweh Himself, they ought to be conducted with due reverence and discretion.
Beside the altar - What is called “the holy place” in Leviticus 10:13, Leviticus 10:17 : it should be rather, a holy place, any part of the holy precinct, as distinguished from a merely “clean place” Leviticus 10:14, either within or without the court of the tabernacle.
Wave breast and heave shoulder - See Leviticus 7:30 note.
12 And Moses spake unto Aaron, and unto Eleazar and unto Ithamar, his sons that were left, Take the meat offering that remaineth of the offerings of the LORD made by fire, and eat it without leaven beside the altar: for it is most holy:
13 And ye shall eat it in the holy place, because it is thy due, and thy sons' due, of the sacrifices of the LORD made by fire: for so I am commanded.
14 And the wave breast and heave shoulder shall ye eat in a clean place; thou, and thy sons, and thy daughters with thee: for they be thy due, and thy sons' due, which are given out of the sacrifices of peace offerings of the children of Israel.
15 The heave shoulder and the wave breast shall they bring with the offerings made by fire of the fat, to wave it for a wave offering before the LORD; and it shall be thine, and thy sons' with thee, by a statute for ever; as the LORD hath commanded.