One of the stranger customs in Judaism is that on the seventh day of Sukkot, Hoshana Rabbah, we takes some aravot (willow branches) and beat them on the ground, havatat aravot. The Rambam (Laws of lulav 7:22) writes that a person is to take one or more branches and to hit them on the floor or on an item, two or three times without reciting a blessing. The Shulchan Arukh (664:4) follows this ruling, while the Mishnah Berurah (664:19) quotes the Ari that one should hit the branches five times on the floor. What is the point of this custom?
The Mishnah (Sukkah 4:5,6, Talmud Sukkah 45a) records the ceremony in the Bet ha-Mikdash of hoshannot, that people circled around the altar with aravot on each of the seven days of the holiday of Sukkot, but it does not mention beating the aravot. Instead, at the end of its discussion of the hoshannot ceremony, the Mishnah quotes Rebbi Yochanon ben Berokah that the seventh day of Sukkot was called the day of the beating of the palm branches since the people would beat palm branches on the ground by the side of the altar. Why all of a sudden is the Mishnah referring to palm branches in the middle of the ceremony of the aravot?
The Tosefta (Sukkah 3:1, also Talmud Sukkah 43b) records that when Hoshana Rabbah was on Shabbat there was an argument between the Rabbis and the Boethusians whether the aravot could be beaten, the Rabbis said yes while the Boethusians said no. This source indicates that really it was aravot that were beaten on the seventh day and not palm branches. (Maybe to cover up this argument the Mishnah switched the aravot to palm branches.) Note that because of this argument the calendar was fixed that Hoshana Rabbah could not come out on Shabbat, which suggests that the Rabbis agreed with the Boethusians that it was wrong to beat the aravot on Shabbat but that they allowed it due to the demand of the people. Yet, still what is the reason for beating the aravot in the Bet ha-Mikdash?
Bradley Shavit Artson (1996) reviews several reasons that have been suggested for beating the aravot. One reason he quotes from Abraham Milligram that is that beating was connected with rain bringing rituals. Artson rejects this reason since "there is nothing extant to indicate why the willow beating would symbolize rain." Instead, he suggests that the beating was to make the aravot pasul, no longer usable. A proof for this idea is that the following Mishnah (Sukkah 4:7) records that after the hoshannot ceremony, the children would separate the lulav from the other items and eat the etrogim. Yet, why only beat the aravot and not the hadasim or lulavim?
My guess is that the beating of the aravot is related to the prayers for rain during Sukkot and it must be connected with the hoshannot ceremony of circling the altar. In our discussion, "Aravot in the Bet ha-Mikdash," (https://lobashamayim.blogspot.co.il/2017/09/aravot-in-bet-ha-mikdash.html) I suggested that the circling of the aravot was to make the Bet ha-Mikdash green. The idea was that by making the altar green, this was a prayer that there should be rain to make the land green. I suspect that the beating of the willows had the same purpose, to make the altar green, as the beating was a way of painting the altar green. This was done on the last day of Sukkot to leave the altar green since the people would no longer be circling the altar with aravot. This explanation offers a reason why the Boethusians objected to this practice only on Shabbat since this beating was a form of painting the altar, and then they would argue that it was forbidden to paint on Shabbat. Also, maybe the Mishnah switched the beating from aravot to palm branches since palm branches would not leave stains.