In slight contradiction to the accepted answer, the Gregorian calendar is designed to have the March equinox occur on March 20, plus or minus a day, not March 21. Christian churches use March 21 as the ecclesiastic equinox. The reason for using March 21 simplifies the calculation of the date of Easter. The March equinox advances by about 5 hours from the previous year's March equinox in non leap year years but retreats by about 19 hours from the previous year's March equinox in the case of a leap year.
Regarding the question itself,
AFAIK the summer and and winter solstices are based on longest day and longest night doesn't fall on 1st of Jan and July 1st because we consider the day to begin and end when the middle of the sun is over the horizon but when it stars to rise and after if has completely set.
The solstices occur a bit over a week before the first of January and the first of July. The calendar used by many nations are based on the calendar reformations mandated by Julius Caesar. Like many things political, shifting the start of the year to the first of January was a bit arbitrary.
So how come it doesn't fall middle of the year, 365/4 = 91 days into the year.
The astronomical seasons are not equal in length. The time span between the December solstice and the March equinox (northern hemisphere astronomical winter / southern hemisphere astronomical summer) currently is about 88.99 days and is getting shorter as perihelion advances by about a day every 70 years. The time span between the June solstice and the September equinox (northern hemisphere astronomical summer / southern hemisphere astronomical winter) currently is about 93.66 days and is getting longer as aphelion likewise advances by about a day every 70 years.