Does anyone remember that show The Tribe about all the kids left over after a disease kills all the adults? They kids banded together in tribes based on their needs, interests, and location (e.g.: The Mall Rats). You could tell a lot about a person in that world based on how they looked and what they wore.
In the post-apocalypse you might want people to know who you’re allied with or where you’re from.
In child development, the time between infancy and kindergarten is one of the most important. During this time, children learn the basics, like the alphabet and numbers. It’s also when they learn basic (but important) life skills, like how to go to the bathroom in a place other than their pants.
This won’t change after the apocalypse. Those crucial early years will remain just as crucial, though the education system will probably change.