Emor

(English Translation cont (from chabad.org))
Three [questions and answers] were given regarding each matter. Why was all this necessary? Because of those who erred who departed from the community of Israel in the Second Temple [era].They maintained that the Torah's expression [Leviticus 23:11]: "From the day following the Sabbath" [should be understood literally, as referring to] the Sabbath of the week. Nevertheless, according to the Oral Tradition, [our Sages] derived that the intent is not the Sabbath, but the festival. And so, was understood at all times by the prophets and the Sanhedrin in every generation. They would have the omer waved on the sixteenth of Nisan whether it fell during the week or on the Sabbath.
[This interpretation is also reflected in the Written Torah itself,] for it is written in the Torah [ibid.:14]: "You shall not eat bread, roasted grain, or kernels of grain until this self-same day." And [Joshua 4:11] states: "And they ate from the produce of the land on the day after Pesach, matzot and roasted grain." And if one would presume that in that year Pesach fell on the Sabbath as these fools have supposed, why would Scripture make the license for them to eat new grain dependent on a factor that is not fundamental, nor the true cause, but mere coincendence. Instead, since [Scripture] made the matter dependent on "the day after Pesach," it is clear that the day after Pesach is the cause that permits new grain [to be eaten] and no attention is paid to the day of the week [on which it falls].

Likkutei Sichos
Starting on the day after of the day of rest: As we have just explained, the counting of the omer is an arduous process of self-refinement for which each of us must assume personal responsibility. Nonetheless, since “taming” the human/animal soul requires going against its nature, we would not be able to undertake this challenge without some initial propulsion from God. This is why the count can only begin on the second day of Passover, after God has redeemed us from the restrictions of nature by taking us out of our collective and individual Egypt.
The Torah therefore, in this verse, refers to the first day of Passover as “the day of rest,” i.e., the Sabbath. As the last day of the week of creation, the Sabbath is the pinnacle of time. Nevertheless, inasmuch as both space and time are the contexts within which God created this finite world, even the Sabbath is finite. By telling us to begin to count the omer from “the day after the Sabbath,” the Torah is ensuring that we set upon this task supported by God’s transcendent energy, which is beyond the limits of time.
Since the revelation of this transcendent Divinity occurs specifically on the first day of Passover, it is clear that the Torah means for us to begin counting the omer on the day after that day rather than on the day after the Sabbath (i.e., Sunday), as a literal reading of the verse might imply.
Nonetheless, the Boethusians, a heretical Jewish group who lived toward the end of the Second Temple era, took this phrase literally and therefore maintained exactly that. They insisted that counting the omer should always begin on a Sunday. In order to force the Temple service to follow their interpretation of this verse, they even went so far as to try to rig the rabbinical court’s declarations of the New Month so Passover would occur on the Sabbath. The sages of the Talmud, in defense of the understanding of this verse as passed down from Moses (i.e., that the “Sabbath” referred to in this verse refers to the rest observed on the first day of Passover) offered no less than five separate textual references disproving the assertion of the Boethusians.
The reason why the Boethusians were disposed to insist that counting the omer begin on a Sunday was because they felt that the only way such a lofty endeavor could be attempted was if it was preceded immediately by the spirituality of the Sabbath. True, we are enjoined to celebrate both the Sabbath and the festivals with fine food and fine clothing, but whereas the sublime sanctity of the Sabbath elevates these material indulgences to experiences of spiritual delight, the spirit of the festivals is more that of joy and elation. Thus, the requirement to eat festive meals is greater on the festivals than it is on the Sabbath; we even have to be warned against undesirable effects of overindulgence. The Boethusians therefore reasoned that such sensual excess could hardly be considered conducive to undertaking a process of spiritual growth.
However, they missed the entire point. The reason the Torah requires us to begin the counting of the omer after some other event or day, as explained above, is because we cannot accomplish this supernatural transformation of the human/animal soul solely with our own strengths; we need the added help of God’s transcendence. Our own self-refinement is of no avail in eliciting this transcendent Divinity. The only way we can invoke God’s supernatural aid is by transcending our own natural limitations—including those of our own intellect—i.e., through our supra-rational submission to God’s will. On the contrary, our belief in the power of God’s transcendence is expressed specifically by performing the seemingly impossible or irrational feat of infusing physical reality with Divine consciousness—as we do when we celebrate God’s festivals through physical means.