How do we know that ממחרת השבת means from the first day of Pesach and not the seventh?
Don't they both deserve to be called שבת?
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Menachot 65b cites 4 Tan'aim who provide 4 explanations to reconcile these 2 verses:
Rabbi Yishmael says there is another refutation of the Boethusian interpretation. The Torah said: Bring the omer offering on the festival on Passover and the two loaves on Shavuot. Just as there, with regard to the offering on the festival of Shavuot, the two loaves are brought at the beginning of the Festival, as it's written the day after the Shabbat (Tosfot explains that we see as if Shavuot has several daya because its Korban Chagiga can be offered not only on the day of Shavuot but during 7 days that begin on Shavuot, as the chagiga of Pesah) , so too here, with regard to the festival of Passover, the omer must be brought at the beginning of the Festival. If the omer were to always be brought on a Sunday, this might occur at the end of the festival of Passover. For example, if Passover started on a Monday, the omer would be brought only on the next Sunday, at the end of the Festival. [Note: The translation is from sefaria, except the part in Italic, which I modified according to the comments of Rashi and Tosfot.]
I pasted just R' Yishmael's opinion- to see the rest, please see here in Sefaria.
(1): Torah speaks in days, 50 days and in weeks, 7 weeks, weeks when Yom Tov falls on Shabbat, days when it falls in the middle of the week.
(2): The Torah says, Count for yourself, the count needs to be made by the Beth Din, if it was a standard week everyone can count without the help of the Beth Din.
(3): Torah says, count days and sanctify the month, cound days and sanctify Shavuot, if Shavuot would be after Shabbat, how can you reach it by a count?
(4): There is a parallel between The Omer and Shtee Halechem, the second is at the beginning of a festival, the first too must to fall at the beginning of a festival.
(5): The first festival is called Shabbat, and the second is called Shabbat, the second is at the beginning of the festival, the first is also at the beginning of the festival.