Why the Fifteenth and Not the First

The Mishnah preserves a disagreement between the school of Shammai and the school of Hillel about which day of Shevat begins the year for trees. Shammai says the first; Hillel says the fifteenth. Hillel's ruling is the one that stands, as it usually does.

The reasoning offered afterwards turns on rainfall. Most of the season's rain in the land of Israel has fallen by mid-Shevat, and the tree's new growth is held to draw on that water rather than the previous year's. Setting the boundary a fortnight later gives the rains time to arrive before the year is declared new.

The choice has a side effect worth noticing. A date on the fifteenth of a lunar month is a full moon. The other Jewish festivals that fall at full moon, Passover, Sukkot, are major pilgrimage feasts, and the coincidence gave later generations a hook: a day called a new year, falling at full moon, looked like it ought to be celebrated. The rabbinic ruling that produced that appearance was not trying to produce it.