Based on the above, it is possible to explain why Tosafos raise the question (see sec. 1 above)וְעַל פִּי זֶה יֵשׁ לְבָאֵר מַה שֶּׁהִקְשׁוּ הַתּוֹסְפוֹת
that the Talmud should have derived the fact that the Jews came to the Sinai desert on Rosh Chodesh from a gezeirah shavah based on the word midbar:דַּהֲוָה לֵיהּ לְמֵילַף מִדְבָּר מִמִּדְבָּר,
For the fact that the Jews attained the level of midbar on Rosh Chodesh Sivan seeminglyכִּי זֶה שֶׁבְּרֹאשׁ חֹדֶשׁ סִיוָן בָּאוּ לִבְחִינַת מִדְבָּר
represents a loftier level of bittul than that alluded to by Rosh Chodesh being referred to as hayom hazeh, “this day.”הוּא בִּטּוּל נַעֲלֶה יוֹתֵר מִזֶּה שֶׁרֹאשׁ חֹדֶשׁ נִקְרָא יוֹם הַזֶּה.
For “this day” implies that a person’s identity remains intactדְּעִנְיַן יוֹם הַזֶּה הוּא שֶׁהוּא בִּמְצִיאוּת
(indeed, his identity is extended outward and expresses itself, as implied by the word “day”);1(וְעַד לִמְצִיאוּת דְּהִתְפַּשְּׁטוּת, יוֹם)
but his identity is characterized by bittul, (as alluded to by the word “this”).אֶלָּא שֶׁהַמְּצִיאוּת שֶׁלּוֹ הִיא בְּבִטּוּל (הַזֶּה),
In contrast, the Jews’ attainment, on Rosh Chodesh Sivan, of the level of bittul alluded to by midbar, “the desert,”מַה שֶּׁאֵין כֵּן זֶה שֶׁבְּרֹאשׁ חֹדֶשׁ סִיוָן בָּאוּ לִבְחִינַת מִדְבָּר
[i.e., that the person’s speech is not his own at all,2[שֶׁהַדִּבּוּר שֶׁלּוֹ אֵינוֹ דִּבּוּר עַצְמוֹ כְּלָל,
and that his mouth is nothing more than a medium for the word of G‑d speaking through him,וּפֶה הָאָדָם הוּא רַק כְּלִי לִדְבַר הֲוָיָ' הַמְדַבֵּר עַל יָדוֹ,
like the word of G‑d uttered by a prophet,]3 who is speaking G‑d’s words and not his own,וְעַל דֶּרֶךְ דְּבַר ה' בְּפִי הַנָּבִיא]
reflects how the the person’s entire identity is batel.הוּא בִּטּוּל הַמְּצִיאוּת.
Since the primary positive quality of Rosh Chodesh Sivan is that on that day the Jews attained the level of utter and consummate bittul alluded to by a desert,וְכֵיוָן שֶׁעִקַּר הַמַּעֲלָה דְּרֹאשׁ חֹדֶשׁ סִיוָן הוּא שֶׁבּוֹ בָּאוּ לְהַבִּטּוּל דְּמִדְבָּר,
accordingly, it is possible to say that the Torah was alluding (to the fact that this level was reached on Rosh Chodesh Sivan)לָכֵן מָקוֹם לוֹמַר שֶׁהָרֶמֶז בַּכָּתוּב (שֶׁזֶּה הָיָה בְּרֹאשׁ חֹדֶשׁ סִיוָן)
by its use of the word midbar.4הוּא בְּתֵבַת מִדְבָּר.
Nevertheless, the Gemara derives the gezeirah shavah specifically from the words bayom hazeh, “on this day,”וְזֶה שֶׁהַלִּמּוּד בַּגְּמָרָא הוּא מִבַּיּוֹם הַזֶּה, הוּא,
because in truth, the level of Divine service alluded to by bayom hazeh, which was attained on Rosh Chodesh Sivan,כִּי הָעִנְיָן דְּיוֹם הַזֶּה שֶׁבְּרֹאשׁ חֹדֶשׁ סִיוָן הוּא
surpasses even the utter bittul alluded to by midbar, as will soon be explained.נַעֲלֶה יוֹתֵר גַּם מֵהַבִּטּוּל דְּמִדְבָּר, כְּדִלְקַמָּן.

Summary

Based on the above, it is possible to explain why Tosafos raise the question that the Talmud should have derived the fact that the Jews came to the Sinai desert on Rosh Chodesh from a gezeirah shavah based on the word midbar: Midbar, “desert,” alludes to a consummate degree of bittul. As explained above, “this day” reflects a level of Divine service in which a person’s identity remains intact; indeed, he even expresses himself, but that self-expression is characterized by bittul. “Desert,” by contrast, implies utter and consummate bittul to the extent that no vestige of personal identity remains. Hence, it is possible to say that the verse was alluding to this loftier level of bittul. Nevertheless, the Gemara derives the gezeirah shavah specifically from the words bayom hazeh, “on this day,” because the level of Divine service alluded to by this phrase surpasses even the utter bittul alluded to by midbar, as will be explained.