Why can't the Shtei HaLechem be baked on Shavuoth?

Question

In Avoth 5:5 we learn that one of the 10 miracles in the Temple was that the Shtei HaLechem - the 2 breads brought on Shavuoth and eaten by the Cohanim - were never found to be invalid:

עֲשָׂרָה נִסִּים נַעֲשׂוּ לַאֲבוֹתֵינוּ בְּבֵית הַמִּקְדָּשׁ ... וְלֹא נִמְצָא פְסוּל בָּעֹמֶר וּבִשְׁתֵּי הַלֶּחֶם וּבְלֶחֶם הַפָּנִים,‏

The Bartenura explains that since they could not be baked on Yom Tov, had they been invalid there would be no way to replace them:

וְלֹא נִמְצָא פְסוּל בָּעֹמֶר וּבִשְׁתֵּי הַלֶּחֶם וּבְלֶחֶם הַפָּנִים. שֶׁאִם הָיָה נִמְצָא בָּהֶם פְּסוּל קֹדֶם מִצְוָתָן לֹא הָיָה אֶפְשָׁר לְהַקְרִיב אֲחֵרִים תַּחְתָּם. שֶׁהָעֹמֶר נִקְצַר בַּלַּיְלָה וְלֹא הָיוּ מַרְבִּים לִקְצֹר. וּשְׁתֵּי הַלֶּחֶם נֶאֱפִים מֵעֶרֶב יוֹם טוֹב וְאֵין אֲפִיָּתָן דּוֹחָה יוֹם טוֹב. וְכֵן לֶחֶם הַפָּנִים נֶאֱפָה מֵעֶרֶב שַׁבָּת‏

I'm wondering why the Shtei-HaLechem couldn't be baked on Yom Tov, why are they different from any other bread that may be baked on Yom Tov?

Answer 1

Pesachim 47a (with translation and elucidation from Sefaria):

שאני התם דאמר קרא לכם לכם ולא לגבוה

The Gemara answers: It is different there, in the case of the two loaves, as the verse says: “No kind of labor shall be done on them, save that which every man must eat, that only may be done for you” (Exodus 12:16). This indicates that it is permitted to cook and bake only “for you,” i.e., for human consumption, and not for the One above, namely for the Temple service.

It's worth noting that this is actually a matter of dispute. R. Shimon b. Gamliel allows one to bake the shtei halechem on Shavuot itself. As the gemara continues:

ולרבן שמעון בן גמליאל דאמר משום רבי שמעון בן הסגן דוחה את יום טוב מאי איכא למימר סבר לה כאבא שאול דאמר לכם לכם ולא לגוים

The Gemara asks: And according to Rabban Shimon ben Gamliel, who said in the name of Rabbi Shimon, son of the deputy High Priest, that baking the shewbread overrides the Festival, what can be said? How does he understand the term: For you? The Gemara answers: He holds in accordance with the opinion of Abba Shaul, who said that this verse should be understood in the following manner: Cooking and baking are permitted for you, and not for gentiles; for the sake of the Temple service, however, they are permitted.