Clearing the Way for Torah Study
When Jews entered Eretz Yisrael they were obligated to bring the first grain that they reaped as a minchat omer flour offering. "You shall bring an omer measure of the first of your reaping unto the kohen" (Vayikra 23:10) says the Torah in introducing this mitzvah.
The Torahs insistence on this barley flour offering being the "first of your reaping" serves as a prohibition against reaping any grain before Pesach, when the grain for the omer is reaped to be processed and offered. We nevertheless find that it was permissible to reap the grain of a field to clear it as a place for people to learn Torah if there was no other space available to seat a large number of Torah students. Where do we see in the words of the Torah such a dispensation?
The answer lies in the Torahs use of the possessive form in the term "your reaping". This is understood by our Sages as an indication that pre-Pesach reaping is forbidden only when it is done for your personal use, but not when that reaping is done for the purpose of fulfilling a mitzvah. A few examples of cutting down grain for the sake of a mitzvah are mentioned in the mishna (Menachot 71a) and one of them is this need to clear a field for the sake of Torah study.
Although it is not clear from our gemara why there was a need for such a large, concentrated area, we may gain a clue from a mishna in Mesechta Shabbat (126b). There we learn that it is permissible to remove on Shabbat four or five crates of straw or grain to make room for Torah study despite the fact that the physical exertion involved is not ordinarily permitted on this day of rest. In his commentary on that mishna Rashi explains that a Torah lecture was to be delivered and a large space was needed for the audience. We may safely assume that this was the situation referred to in our own gemara as justifying an early reaping.
Eating for Atonement
When G-d informed Aharon of all the holy things "reserved from the fire of the altar" which would be consumed by him and his sons a special mention is made of "all the mincha flour offerings" (Bamidbar 18:9). This all-inclusive term is interpreted by our Sages as an indication that even the omer mincha offered to permit use of the new grain and the mincha brought by the husband of a suspected adulteress are also consumed by the kohanim after a kemitza portion of them has been burned on the altar.
Why, the question is raised, would I have thought that the kohanim should be less entitled to enjoy these mincha offerings?
The answer lies in what is written about the consumption of animal meat and loaves used in the sacrificial service in the inauguration of the kohanim. "They shall eat those things with which atonement was made" says the Torah (Shmot 29:33), indicating that the consumption of these sacred items is part of the atonement process.
Had the Torah not spelled out with the word all that these two barley flour mincha offerings were also assigned to the kohanim for consumption we would have assumed that only a mincha which serves as an atonement goes to them because they participate in the atonement process through their eating. The purpose of the mincha of the omer, on the other hand, is not atonement, but a license for enjoying the new crop of grain, and the other minchas purpose is to clarify the guilt or innocence of the suspected adulteress.
The Sefer Hachinuch (Mitzvah 95) explains the role of the kohen eating sacrificial flesh or loaves in terms of the sinner providing "the portions which sustain the teachers of Torah who will pray for him".
While this may be the purpose of the kohen eating in cases where atonement is necessary, the Torah, in its all-inclusive "all" revealed that there are other reasons as well for such an allocation to G-ds servants, and that they apply to the two barley mincha offerings as well.