It's a matter of having statistics that can be compared year-on-year. From the Met Office website:
"The meteorological seasons consist of splitting the seasons into four periods made up of three months each. These seasons are split to coincide with our Gregorian calendar, making it easier for meteorological observing and forecasting to compare seasonal and monthly statistics. By the meteorological calendar, spring will always start on 1 March; ending on 31 May.

The seasons are defined as spring (March, April, May), summer (June, July, August), autumn (September, October, November) and winter (December, January, February)."

It might seem arbitrary, but so is defining the seasons as beginning and ending on solstices and equinoxes. Doing it that way, summer started yesterday. As we've had six amazing weeks of "summery" weather already, that seems slightly absurd, at least this year. Another issue is the actual dates on which solstices and equinoxes fall vary from year to year. It's arbitrary, but doing it in convenient three-month chunks is more consistent.