Weather agencies treat summer as beginning on the first of June, while the calendar marks the solstice weeks later. The two definitions coexist because they are built for different purposes, and only one of them supports statistics.
What the astronomical definition follows
Astronomical seasons are anchored to the tilt of the earth relative to the sun, with boundaries at the solstices and equinoxes.
Those moments are precise instants rather than dates, and they drift within the calendar because the orbital year does not divide evenly into whole days.
The resulting seasons are also unequal in length, since the planet moves at varying speed along its orbit and spends slightly different amounts of time in each quarter.
Why that makes record-keeping awkward
Climate records are kept as monthly totals and averages, which is the unit that station observations have been aggregated into for a very long time.
A season that begins partway through a month cuts those records in half and forces every comparison to be reassembled from daily values.
Worse, if the boundary shifts by a day between years, then two consecutive seasons cover slightly different spans, and any difference between them is partly an artifact of the definition.
How the meteorological convention fixes it
Meteorological seasons are three whole months each, beginning on the first of December, March, June and September.
Each season therefore contains the same calendar days every year, and totals from one year can be set against another without adjustment.
The blocks are also chosen to sit around the annual temperature extremes, so winter brackets the coldest stretch and summer the warmest rather than beginning at them.
Why the seasonal lag justifies the shift
Surface temperature peaks weeks after the sun does, because land and water keep absorbing heat past the solstice before losses catch up.
Starting summer at the solstice would place the hottest weeks in the middle of the season rather than at its start, but starting at the calendar month centers them more usefully.
The convention effectively accepts that the thermal year runs behind the astronomical one, and defines seasons around the temperature curve instead of the orbit.
Where the two definitions genuinely conflict
Reports that a season was the warmest on record almost always use the meteorological definition, since that is how the underlying data is stored.
The same period assessed astronomically would include different days at both ends and could produce a different ranking, particularly in a year with an unusual start or finish.
Neither is wrong, but comparing a figure computed one way against a figure computed the other introduces a mismatch that has nothing to do with the weather.