How it happened that two schools are so close to each other I cannot explain, but when it happened I can comment on.
When San Francisco won the Outside Lands suit against the Feds in 1866 and came into possession of the territory which includes the Richmond District, one of the first things the city did was to survey all that sand, "grid-i-fying" miles and miles of square miles of sand. Streets and avenues and blocks were laid out. Then the city chose "reservations": land reserved to the city for public purposes: schools, fire houses, parks, etc.
By 1875/1876 the reservations were listed in the Municipal Reports, an annual summary of the city's business. That's when the sites for today's Peabody and McCoppin had been chosen and the public informed. At that time there were no schools on the sites.
McCoppin was originally called Park School. It was a one-room school built on its current site in 1896 by volunteer labor for the cost of materials to answer the need for more class rooms for the booming inner Richmond.