According to Song Facts.com, “Graham Nash wrote this. The lyrics deal with the often difficult relationship he had with his father, who spent time in prison.
Jerry Garcia performs the pedal steel guitar part of this track. He had been playing steel guitar for only a short period of time. Garcia played on this album in exchange for harmony lessons for the Grateful Dead, who were at the time recording their acoustic albums Workingman’s Dead and American Beauty.
Graham Nash (from the liner notes of their 1991 boxed set): “The idea is that you write something so personal that every single person on the planet can relate to it. Once it’s there on vinyl it unfolds, outwards, so that it applies to almost any situation. ‘Teach’ started out as a slightly funky English folk song but Stephen (Stills) put a country beat to it and turned it into a hit record.”
Deja Vu (released in 1970) was the first album the band recorded with Neil Young, but Young did not play on this.”
According to Wikipedia and this video, this song was immediately inspired by a Life magazine photograph by Diane Arbus titled “Child with Toy Hand Grenade in Central Park.”
This picture prompted Graham Nash to pen down his thoughts on the social implications of messages given to children about war and other issues as well as his own relationship with his father.