Indeed, according to our approach, the entire matter is well-settled and explained, for they did not sing a song of praise for their own salvation, nor for the downfall of their enemies, but rather for the vengeance of Hashem on the nations that did not call upon His name, and for the restoration of the glory of His blessed name in the world. It turns out that their song did not constitute rejoicing in the downfall of their enemy, as in "Do not rejoice when your enemy falls," because their joy was over the honor of Hashem that was restored through the downfall of the enemies of Hashem who desecrated His name, and in this, a Kiddush Hashem (sanctification of God's name) was made.

Now it is well explained why Hashem restrained the angels from saying a song of praise, but allowed Israel to sing the song. For the angels wanted to sing a song of praise solely for the downfall of the enemy, and this Hashem did not permit, for after all, they too are His creations, even though they are, of course, far less significant than the children of Israel. But Israel did not sing for the downfall of the enemy, nor even for their own salvation, but rather for the restoration of the crown of holiness to the world, and thus they were able to sing a song of praise.