Sforno on Numbers 18:9/ספורנו על במדבר י״ח:ט׳

1מן האש, for all of it was meant for burning on the altar, the priests having no share in it until after the parts which have to be burned up have been burned up. The reason is that the priests’ share is not really theirs, i.e. the sacrificial animal or parts of it does not belong to them, but it belongs to G’d and whatever they may eat, they eat as “guests at G’d’s table,” not in their own right, in Talmudic parlance משלחן גבוה הם אוכלים.