Background
As mentioned in the previous study on burnt offering atonements, there is not much background to Leviticus. This study picks up in Leviticus 2, which further explains why it's good to be the priest, as a continuation of a set of laws which seem to come from out of nowhere.
Sustaining the Priesthood

In Exodus 28:1, we have seen how the priesthood would belong to Aaron and his sons for the generations to come, making it a family-only affair. Exodus 25-31 establish a posh mobile palace for the priests made by the best artisans and with the best materials available. God's priests be adorned in fine cloth, gold, and bells; to give them respect and so that God would not kill them. And we have seen the priests collect money for atonement like a God-directed tax from the entire male adult population.
Now, imagine if you could feast on the best grains and meats without ever having to reap and sow or tend to a herd, or even pay for it. A man has got to eat, and priests are no exception. As we see in Leviticus 2 through Leviticus 7, God's laws provide for the priests there too.
Leviticus 2 covers grain offerings to God. The grains are to already be processed; ground into fine flour (Leviticus 2:1-3), or baked into cakes or wafers (Leviticus 2:4-10), or crushed and fire roasted (Leviticus 2:14-16). Essentially, the grain was to be ready to bake or ready to eat when presented to the priests for an offering. The priests burned a small “memorial portion” for God and then ate the rest themselves.
Leviticus 2:13 goes on to say that all of these grain offerings must be seasoned with salt. This is purely for the flavor, and is therefore additional evidence of these laws being contrived by man. After all, why would God require such a potentially deadly food additive? God would know better. Man would not, at least not for several thousand years.
Regulations regarding offerings continue on to Leviticus 7, but not without Leviticus 6:14-23 strangely repeating some regulations of the grain offerings. (Remember, this was written before electronic word processing, so document organization was a bit flawed at times.)
For sin (Leviticus 6:24-30) and guilt (Leviticus 7:1-10) offerings, the priests get to eat all of the slaughtered animal with the exception of fatty tissues and the kidneys. The priests even get to keep the hides from the animals (Leviticus 7:8)!
By the way, in case you are wondering the difference between guilt and sin offerings, it's like this: guilt offerings made atonement for both unintentional (Leviticus 5:14-19) and intentional (Leviticus 6:1-7) sins, while sin offerings only made atonement for both (Leviticus 5:1-5) unintentional and intentional sins. Clear as mud? And yes, this is true atonement (without Jesus!), as we can see that the guilty party will be forgiven by God in Leviticus 6:7.
Also, did you notice that only males were allowed to eat from the grain, sin, and guilt offerings?
In Leviticus 7:28-36, you find that the priests even get to eat a share of the offerings made for fellowship. While this type of offering was open to any ceremonially clean person to eat, the priests got the breast and the right thigh as payment for performing the offering ceremony.
Yes, the priests ate very well. The Israelite population brought the best of their fields and flocks to offer to God, and to feed the priests. Offerings had to be without defect and of the proper value (Leviticus 6:6). The priests feasted from the labors of others without toil or financial cost.
In fairness, we should expect for priests to have been compensated back then, just as we would today. Certainly, we should not expect God to repay service to Him with a subsistence existence. However, the best foods from the land, the elaborately lush clothing and property, and amassing of monetary wealth of the priesthood as dictated by God's laws seem to put a priority on physical possessions and temporal honors. This detracts from what should have been the great spiritual wealth and honor of being in service to God, but it makes perfect sense for a man-inspired religion.
In that perspective, it is no wonder why some of the poorer masses may have looked with disdain and envy on the Pharisees, a sentiment echoed in Matthew 23:5-7 and Luke 11:43. It should also be no wonder as to why someone, or some group, would have been enticed by that wealth and honor into creating their own religion.
Footnote:
At the end of Leviticus 7, Leviticus 7:37-38 states that all of this information regarding the regulations of offerings were given by God to Moses on Mount Sinai, finally tying these chapters into the storyline asynchronously. In a way, that makes sense because it would not really be necessary for all of the Israelites to agree to the regulations for offerings as part of the Covenant with God. On the other hand, it could be an indication of later authorship, details created after the original story to help fill in the gaps.
Extra Credit Reading:
Check out the regulations regarding the fellowship offerings in Leviticus 7:11-21. Particularly interesting is Leviticus 7:18 where it talks about eating the offering leftovers on the third day will not be credited to the offerer. Then ponder if that section, and that verse in particular, seems a bit too arbitrary and legalistic for God to have commanded.