The ministering angels said before Hashem, "Master of the Universe, why do the Jews not sing Hallel before You on Rosh Hashana and Yom Kippur?" Hashem replied, "Is it possible that when the King is seated on the Throne of Judgement, and the Books of the Living and the Books of the Dead are open before Him, the Jews should sing Hallel?"
What the angels were asking was; because the Jews are commanded to be joyfully confident that they will be inscribed for a good year and thus Rosh Hashana and Yom Kippur are considered Yomim Tovim, therefore it would be fitting for the Jewish People to sing Hallel on those days. To this Hashem responded that, nevertheless, it would be inappropriate for the Jews to sing joyously while the Judgment is in progress.
We need to understand why the angels would have any interest in regard to the Jews singing Hallel; what difference would it make to them whether or not the Jewish People sing Hallel on Rosh Hashana and Yom Kippur?
The Iyun Yaakov explains this phenomenon according to that which the Gemara in Chulin (צא ע"ב) tells us. The Gemara says as follows. The ministering angels do not sing Hallel above until the Jews sing Hallel below, as it is stated, 'When the morning stars [i.e. which alludes to the Jews who are likened to the stars] sing in unison - and only after that - all the heavenly beings shout'. In view of this, we can understand why the Jews' refraining from singing Hallel carries great significance to the angels, for when the Jews refrain from singing Hallel it prevents the angels from singing it, as well.
This explanation seems to be quite reasonable, as it is based upon a concept found in the Gemara in Chulin. Nevertheless, Tosfos in Arachin (י ע"ב) seems to clearly contradict this entire idea. For Tosfos infers from the wording of the angel's question, "why do the Jews not sing Hallel on Rosh Hashana and Yom Kippur?", that only the Jewish People don't sing Hallel on Rosh Hashana and Yom Kippur, but the angels themselves do sing Hallel.
This opinion of Tosfos - that on Rosh Hashana and Yom Kippur the angels sing Hallel while the Jews don't - clearly indicates that the angels' singing Hallel is not dependent upon the Jews singing it, and thus clearly contradicts that which the Gemara teaches us, that the ministering angels do not sing Hallel above until the Jews sing Hallel below. Additionally, according to Tosfos, the angel's query once again begs for explanation; why does the Jewish People singing Hallel matter at all to the ministering angels?
The prophet Yeshaya’s Vision
The prophet Yeshaya (ו' א'-ג') recounts a vision in which he merited to view that which occurs in the Heavenly Court, and he describes it as follows. I saw Hashem sitting upon a high and lofty throne... Seraphim were standing above, at His service... And one called to another and said, "Holy, Holy, Holy is Hashem..."
When the prophet said, 'And one called to another', he is describing how the Seraphim each call to the other to open and lead the praising and glorifying of Hashem's name. The Yalkut Shimoni (ישעי' רמז ת"ד) explains that the reason for this is because each angel feels that the other angel is greater than him, and thus more worthy to initiate the singing of Hashem's praise.
In this same vein we can explain why 'the ministering angels do not sing Hallel above until the Jews sing Hallel below'; the angels wait for the Jewish People to sing Hallel first because they feel that the Jewish People are greater than them, and thus more worthy of initiating the singing of Hashem's Praise and Glory.
In view of this, that the angels wait for the Jews to commence the Hallel only out of respect, we can easily understand that it is only applicable on a day that the Jewish People intend to sing Hallel, but on a day that they won't be singing it, there is no reason for the angels to be dependent on the Jews and to refrain from singing Hallel as well. Therefore, on Rosh Hashana and Yom Kippur, the angels wait for the Jews to begin singing Hallel in order that they too should be able to begin, and when they see that the Jews aren't beginning to sing, it most definitely is very relevant to them, as this compels them to wait as well. They therefore ask Hashem why the Jews aren't singing Hallel, and when Hashem replies that on Rosh Hashana and Yom Kippur it isn't appropriate for the Jews to sing Hallel, the angels take the cue and begin to sing it on their own.
(Zera Shimshon Parshas Emor, Ot Ches)
