It’s a convention. And not one that everyone follows. In Australia we use meteorological seasons, which start on the first of the month. So today is precisely one third of the way through summer.

Because of what you said, I do think that the way we do it is better. It puts the solstice (the day literally called “midsummer”) closer to the middle of the season, and also makes more sense because it puts seasons aligned with the human calendar.