בנפול אויבך אל תשמח, ובכשלו אל יגל לבך
(משלי כ"ד, י"ז)
One of the unique features of prayer on Pessach is the fact that we say a full Hallel only on the first day of the holiday. On chol ha-mo'ed days and on the seventh day of Pessach we say the "half Hallel", a shortened version. This is irregular because on the other two regalim, Sukkot and Shavu'ot, as well as on Chanuka (all 8 days), we say a full Hallel. If Hallel is praise we give to God for delivering us from trouble and performing miracles for us, why only a partial praise is given on most days of Pessach? After all, on the seventh day of Pessach God parted the Red Sea for the Israelites and thus saved them from their Egyptian pursuers, prompting them to sing the Shira; surely this qualifies as an appropriate occasion for us to give full praise to God. So why only a half Hallel?
The redemption of the Israelites from Egypt was accompanied by a lot of misery. Pharaoh's stubborness brought upon his people and country ten plagues, culminating in the killing of all first-borns in the kingdom, including his own son. The parting of the Red Sea meant not only the safe passage of the Israelites but also the drowning of all of Egypt's army. Many human lives were lost during the Exodus.
The Gemarah in Megillah (10:) tells us the following story. After the drama of the Red Sea, when the danger was over and the Egyptians lay dead at the bottom of the sea, the angels up above wanted to sing out to God to praise him for the great miracle he had performed for his people. God silences them by asking a rhetorical question: "The works of my hands are drowning in the sea, and you wish to sing?!".
God teaches the angels (and us) that one should not rejoice over the death of human beings, even if they are the enemy. True, sometimes it is necessary to fight and to win, and in the process lives are inevitably lost, but this is no reason for singing out and praising the occasion. One should regard all loss of human life as a tragedy. This idea was espoused by the "wisest of all men", king Shlomo. In Mishley he writes:
Rejoice not when your enemy falls, and let not your heart be glad when he stumbles.
(Mishley, 24, 17)
The Meshech Chokhma, Rabbi Meir Simcha HaCohen, explains this rule in his commentary to the Torah (Shemot 12, 15). He says many people and religions dedicate a "day of victory" to commemorate the fall of their enemies, but Jews do not. Their days of celebration are not for celebrating the fall of the enemy, but rather the salvation of the Jews. Pessach is for celebrating the redemption from slavery; Chanukah is for celebrating the miracle of the oil in the temple; and Purim is for celebrating the miracle of being saved from Haman's decree. Song and praise are therefore reserved for being saved from trouble, not for the fall of the other side. Indeed, we have an obligation to praise God, but we must frame that obligation in the right context.
Now we understand the reason for the half Hallel in Pessach. On the first day, we say a full Hallel to praise God for the redemption from Egypt. But on the seventh day, we do not say it because we wish to express restraint and repress our feelings of joy in light of the great loss of human life that accompanied the miracle at the Red Sea. We do so by saying the praise, but not in its entirety. (The reason that in chol ha-mo'ed we say a half Hallel is that we do not want to make chol ha-mo'ed seem more important than a full holiday, i.e. the seventh day of Pessach).
The idea for this Thought is from R. Avraham Rivlin of Eretz Chemda