When do the seasons start?
Equinoxes and solstices with exact date and time for any year, and a countdown to the next astronomical season.
Why the date changes every year
Astronomical seasons start when the Sun reaches precise points of the orbit (equinoxes and solstices): since the solar year isn't a whole number of days, the instant drifts by about 6 hours per year, and leap years pull it back. That's why spring can start on March 19, 20 or 21.
Astronomical vs meteorological
Meteorological seasons, used in climate statistics, always start on the 1st of the month (March 1, June 1, September 1, December 1). Astronomical ones — these — follow the Sun, with minute-accurate times (Meeus' algorithms).