And, according to Wikipedia, farming has nothing to do with it:
The origins of the summer holiday break are often believed to be rooted in
agriculture. It is widely believed that the school calendar follows the
agrarian farming calendar because during the settlement of the United
States, the nation primarily consisted of a farming population. This belief
maintains that the current school calendar has a two to three-month break so
that children could assume the necessary tasks of planting and harvesting
crops. However, planting of most crops occurred in the spring and harvest
occurred in the fall. Rural schools would often break for spring and fall
seasons, but continue schooling throughout the summer.