Gifts of appreciation
וזה יהיה משפט הכהנים מאת העם מאת זבחי הזבח אם-שור אם-שה ונתן לכהן הזרע והלחיים והקבה
This will be the law for the Kohanim: Those from the nation who slaughter a cow or a sheep will give to the Kohen the [animal’s] shoulder, cheeks, and stomach
Hashem’s chosen family for the Temple service is the Kohanim, the descendants of Aharon. What comes with this responsibility is certain gifts. The rest of the nation are commanded to give some of the produce to Kohanim, as well as the choicest parts of their animals. The gemarra asks a simple question: If a Kohen grabs away the gifts owed to them from the original owner, is that showing that they cherish the mitzvah? Or is that disrespectful to the mitzvah. The gemarra answers that the Torah says for the non-Kohen to give the animal parts to the Kohen, not that the Kohen should take it.
Regardless, we see from here that there is a concept of cherishing the mitzvah of the Kohanic gifts. If there wasn’t, the question wouldn’t have even gotten started. How can we understand this? These gifts have no inherent holiness. This is demonstrated by the fact that the Kohen who receives these them can even feed them to their pets. They don’t get their own blessing upon consumption. Why then would receiving these gifts have any concept of cherishing the mitzvah, to the point that there was a question if a Kohen should grab them away from their original owner?
We have to say that it is incumbent upon the Kohen to recognize and appreciate the gifts that Hashem with His great kindness has granted him. Therefore, the Kohen should run after these gifts, in order to show this appreciation. Since Hashem gave the Kohen these gifts, they are very dear and precious in his eyes. This is the concept of cherishing the mitzvah. This is why we are taught that these gifts have to be eaten roasted with mustard, the way that royalty eats them. This is all to demonstrate how precious these gifts which Hashem honored the Kohen with are.
With this we can now understand a puzzling story related in the gemarra. Rav Chisda was holding two Kohanic gifts from a slaughtered cow. He said that anyone who can share with him a new teaching of his teacher Rav, that he’d give them these gifts. Rava bar Mechasia told him that Rav said that whoever gives someone a gift, they must inform them. We learn this behavior from Hashem Himself, from when He gave us the gift of Shabbos. Rav Chisda gave him these two gifts in appreciation for this new teaching. Rava bar Mechasia told Rav Chisda that if Rav’s teachings are so dear to him, he’ll share with him another teaching. Rav said that an article of clothing is worth more to the one wearing it than to others. Rav Chisda asked did Rav really teach this? If so, this latter teaching is better than the first. He said that if he had another animal gift he would have given it to him as well.
There are many questions on this story. Why was Rav Chisda specifically looking for a teaching from Rav? He wouldn’t give a gift to someone who told him a teaching from someone else? Why was there a need for an incentive? If someone truly had a new teaching from Rav, they’d share it for free. Why did Rav Chisda conclude by saying if he had another Kohanic gift he would give it in appreciation for the second teaching? He couldn’t give him something else? Rav Chisda was known to be very wealthy. Why was the second teaching considered better than the first? The first is a matter of halacha and proper practice, whereas the second is just a fact of nature.
Rashi explains that the two Kohanic gifts that Rav Chisda received were really two sets of cow shoulders, cheeks, and stomachs. Although usually it is better to give each animal part to a different Kohen, a person could decide to give everything to the same Kohen. The fact that Rav Chisda accepted so many animal parts shows that he must have cherished this mitzvah. Further, he announced that whoever would teach him something new that Rav said would receive these gifts. This statement had two implications. It showed that he wasn’t really interested in eating them, and only had them due to his cherishing the mitzvah. As well, he was showing that he wasn’t totally uninterested in them, that he would be willing to give them away to anyone. He made it dependent on someone who could share with him a new teaching. This was due to him also cherishing teachings from his teacher Rav. This connection is why he focused on giving away Kohanic gifts, as opposed to anything else.
This also explains why Rava bar Mechasia chose to specifically share a teaching about receiving gifts. Hashem gave us the gift of Shabbos, because He wants to sanctify and glorify us. Therefore, we need to accept this gift by cherishing and appreciating it. This is very similar to the situation with Rav Chisda, who showed how much he cherished the Kohanic gifts that he was entitled. It was because they were given to him by Hashem, who wanted to sanctify and glorify the Kohanim.
 Based on Be’er Yosef to Deuteronomy 18:3
 Deuteronomy loc. cit.
 Chullin 133a
 Tosefta Chullin 9:2
 Mishneh Torah Hilchos Bechorim 9:20; Shulchan Aruch Yoreh Deah 61:13
 Unlike offerings, which get the blessing of אשר קדשנו במצוותיו וצונו לאכול את הזבח (Rashi to Berachos 48b s.v. כי הוא יברך, Zevachim 37a s.v. בירך and to I Samuel 9:13. See also Mishneh Torah Hilchos Bikkurim 1:2)
 Chullin 132b; Mishneh Torah loc. cit. 9:22; Shulchan Aruch loc. cit. § 12
 Shabbos 10b
 מילתא אלבישייהו יקירא. Translated according to Rashi ad. loc.
 Moed Kattan 28a. Even if this occurred during the time that he was originally poor (Shabbos 140b), why did Rav Chisda specify a gift given to Kohanim?
 The Be’er Yosef also brings from Hagahos Aharon to Ein Yaakov ad. loc. the question of how was it permissible to take payment for teaching Torah (see Nedarim 37a)?
 Shabbos loc. cit.
 Chullin loc. cit. Rav Chisda himself said this
 Mishneh Torah loc. cit. § 17
 The Be’er Yosef points out that this doesn’t seem like Abaye (Chullin 133a) who concluded that it is better for a Kohen to even avoid accepting such gifts. The Be’er Yosef’s son suggests that the Rambam (Mishneh Torah loc. cit. § 22) was bothered with this question, which is why he ruled that בזמן שהם רבים בבית המטבחיים הצנועים מושכין ידיהם והגרגרנים נוטלים. He added that it is better to avoid accepting only when there is a crowd of people trying to take, which has no source anywhere else (see the Derisha ad. loc. who asks this on the Tur ad. loc. The Tur is seemingly just quoting the Rambam. The Derisha doesn’t seem to realize that the Rambam said this, especially since he puts the Rambam in the list of those who didn’t say this; perhaps it’s a typo). He was bothered how could Rav Chisda have so many gifts, and he answers that it was a case where there was no crowd.
 The Maharsha ad. loc. is bothered that Rava bar Mechasia brought down many teachings from Rav. Why did he tell Rav Chisda specifically this one? The Be’er Yosef provides this answer
 See the Be’er Yosef ad. loc. § 4 who addresses what was so great about the second teaching Rava bar Mechasia shared as opposed to the first. The explanation is based on Kiddushin 8a, which has interesting ramifications for the laws of pidyon haben. He also explains why Rav Chisda asked if this was really a teaching of Rav or not