For Chanukah, Bet Shamai says that on the 1st night we start with 8 candles and each successive night one less. Bet Hillel says we start with 1 and increase each successive night.

Why was there no debate about how to count the days of the Omer, similar to the debate about Chanukah "counting"?

I can see support for both sides. One can view it as, "Wow! It's been so many days since G-d exiled us from slavery in Egypt." Whereas another view is, "Wow! Only X more days until we receive the Torah (so we would count downwards)."

Also, Chanukah is a Rabbinic holiday. I would think that if they wanted to debate counting, they would emphasize Shavu'ot being a Torah holiday.

I am aware that the Torah verse says that you should count 50 days. But, AFAIK, there is nothing specific that says HOW to count, unless I missed something.

Chanuka is inherently connected to Sukkot where the Musaf offering includes a "countdown" of bulls. Sefirat HaOmer, on the other hand, is a biblical command to count 50 days from the offering of the Korban Omer which only makes sense incrementally since the actual date of the latter korban of the shtei halechem is dependent on that of the former of the omer.

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The verses regarding the mitzvah of counting read:

Leviticus 23:15-16:

וּסְפַרְתֶּ֤ם לָכֶם֙ מִמָּחֳרַ֣ת הַשַּׁבָּ֔ת מִיּוֹם֙ הֲבִ֣יאֲכֶ֔ם אֶת־עֹ֖מֶר הַתְּנוּפָ֑ה שֶׁ֥בַע שַׁבָּת֖וֹת תְּמִימֹ֥ת תִּהְיֶֽינָה׃ עַ֣ד מִֽמָּחֳרַ֤ת הַשַּׁבָּת֙ הַשְּׁבִיעִ֔ת תִּסְפְּר֖וּ חֲמִשִּׁ֣ים י֑וֹם וְהִקְרַבְתֶּ֛ם מִנְחָ֥ה חֲדָשָׁ֖ה לַיהוָֽה׃

And ye shall count unto you from the morrow after the day of rest, from the day that ye brought the sheaf of the waving; seven weeks shall there be complete; even unto the morrow after the seventh week shall ye number fifty days; and ye shall present a new meal-offering unto the LORD.

Within the verses, there is a progression as well as a specific number. It states to start from the day of bringing the omer offering and at the end of the counting, you will reach specifically 50 days on the day after having counted 7 full weeks.

If we were to count downwards, we would have the same quantity but would not reach those specific numbers. E.g. we would be at day "1".

Rambam writes in Guide for the Perplexed 3:43

The Feast of Weeks is the anniversary of the Revelation on Mount Sinai. In order to raise the importance of this day, we count the days that pass since the preceding festival, just as one who expects his most intimate friend on a certain day counts the days and even the hours. This is the reason why we count the days that pass since the offering of the Omer, between the anniversary of our departure from Egypt and the anniversary of the Lawgiving. The latter was the aim and object of the exodus from Egypt, and thus God said, "I brought you unto myself" (Exod. xix. 4). (Friedlander translation)

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