Earlier quoted context omitted.
Why would that be considered the first day of Fall? Even taking a purely astronomical perspective, the autumnal equinox would be the center of Fall, not the beginning.
Because https://en.wikipedia.org/wiki/Seasonal_lag
Quoting from your link:
> seasonal lag is not "seasonally symmetric"; that is, the period between the winter solstice and thermal midwinter (coldest time) is not the same as between the summer solstice and thermal midsummer (hottest time).
> In mid-latitude continental climates, [seasonal lag] is approximately 20–25 days in winter and 25–35 days in summer.
> there is no meteorological reason for designating these dates as the first days of their respective seasons.