Question: Why do we start counting sefirat ha’omer in chutz la’aretz on the second night of Pesach when the omer in the times of the Beit Hamikdash was cut on Chol HaMoed?
Answer: Your question is, indeed, intriguing and worthy of proper discussion. We begin by noting that we start counting sefirat ha’omer on the eve of the 16th of Nissan due to the Torah’s specific instruction in Parshat Emor (Leviticus 23:15): “U’sefartem lachem mimochorat HaShabbat miyom haviachem et omer hatenufah sheva shabattot temimot tiyenah – You shall count for yourselves from the morrow of the Sabbath day from the day you bring the omer waving, seven complete weeks shall they be.” Rashi (ad loc.) explains that “the Sabbath day” means the first festival day – that is, the first day of Pesach.
The Torah establishes the day of Pesach in Leviticus 23:5-7: “Bachodesh harishon be’arba’ah asar lachodesh bein ha’arbayim Pesach l’Hashem. U’vachamisha asar yom lachodesh hazeh chag hamatzot l’Hashem shiv’at yamim matzot to’chelu. Bayom harishon mikra kodesh yihyeh lachem kol melechet avodah lo ta’asu – In the first month, on the 14th day of the month in the afternoon, is the time of the Pesach offering to Hashem. And on the 15th day of this month is the Festival of Matzot to Hashem; you shall eat matzot for a seven-day period. On the first day you shall have a holy convocation; you shall do no laborious work.”
Thus, we see that Pesach commences on the 15th day of the first month, and we therefore start cutting the barley and bring the omer offering on the 16th, as per the passuk quoted above.
But your question is a good one and is discussed in the fine halachic work of Rav Zvi Cohen, Sefirat Ha’omer – Halachot U’Minhagim Hashalem (available in many bookstores or directly from the author at 17 Rashbam Street, Bnei Brak 51600, Israel).
Rav Cohen notes the following question asked by the Kesef Mishneh (Hilchot Sukkah 6:13, cited by the Magen Avraham, Orach Chayim 489:1, and in Kaf Hachayyim, ad loc. 489:2): “How do we [count] sefirah on the second day of the holiday [in the diaspora] without worrying about demeaning the holiday? For that very reason we do not make a blessing on [eating in] the sukkah on the eighth day [of Sukkot], Shemini Atzeret [in the diaspora], which is a ‘sefeika deyoma – a doubtful day’ – [i.e., it is questionable whether it is] the seventh day of Sukkot, which is Chol HaMoed, or Shemini Atzeret, a festival day.”
The Gemara (Sukkah 47a) concludes its discussion of eating in the sukkah on Shemini Atzeret with the following ruling: “Indeed, we do sit in the sukkah on [Shemini Atzeret], but we do not utter the blessing leishev basukkah.” We don’t do so because we know nowadays when the real day of Sukkot is (as the Gemara [Bezah 4b] says: “yad’inan bike’via de’yarcha”). The only reason we keep the extra day of Sukkot is because the Gemara exhorts us to follow the custom of our fathers. Thus, we continue observing two days of the holiday in the diaspora, just as we did before Hillel the Second established the fixed calendar (which established the exact dates of all holidays for thousands of years, removing any doubt as to when each one starts).
The Gemara states that we don’t say leishev basukkah on Shemini Atzeret because we would be demeaning the holiday if we did. Making the berachah would imply that the day is not actually a festive day – Shemini Atzeret – but rather Chol HaMoed of Sukkot. We might then accidentally violate the holiday by performing labors that are prohibited on festival days.