“…And Miriam, the prophetess, Aharon’s sister, took a tambourine in her hand, and all the women came out after her with tambourines and with dancing….- Shemot 15:20

וַתִּקַּח מִרְיָם הַנְּבִיאָה אֲחוֹת אַהֲרֹן אֶת הַתֹּף בְּיָדָהּ וַתֵּצֶאןָ כָל הַנָּשִׁים אַחֲרֶיהָ בְּתֻפִּים וּבִמְחֹלֹת – שמות טו, כ

The drowning of the Egyptians in the sea (after Bnei Yisrael had safely passed through) brought a complete end to the Egyptian exile and oppression, whereupon the Jews burst into song to thank G-d for their Redemption. The Torah tells us that the women, led by Miriam, surpassed even the men in their celebration; whereas the men only sang, the women also danced and played musical instruments.

The women’s rejoicing was greater than the men’s because their suffering in Egypt had also been greater. For harsher than the backbreaking labor that the Egyptians inflicted upon Bnei Yisreal, were Pharaoh’s decrees regarding the Jewish children. Most notoriously, Pharaoh decreed that the baby boys should all be drowned, and later, Pharaoh bathed in the blood of Jewish children when he was ill, as related in the Midrash (Shemos Rabbah 1:34). Though these decrees obviously caused anguish for all of Bnei Yisrael, but the pain of such experiences is naturally experienced by the child’s mother even more profoundly than by the father. Since the women’s suffering in Egypt had been more painful than the men’s, their joy upon the Redemption was commensurately greater than the men’s as well.

This idea is also highlighted by the fact that the women’s rejoicing was led by Miriam, whose very name reflected the bitterness of exile; the root of מרים, Miriam, is the Hebrew word מר, mar, which means bitter (see Shemos Rabbah 26:1). Our Sages tell us that as a young girl Miriam had prophesied about the Redemption (see Rashi on our verse), a prophecy whose fulfillment she only witnessed more than eighty years later. Having lived her life in painful anticipation of the end of the bitter exile, Miriam’s joy upon the Redemption knew no bounds, and she now naturally led the women in their exceptionally joyous celebration.

—Likkutei Sichos vol. 1, pp. 139-140 & Sefer Hasichos 5752 vol. 1, pp. 303-304)