Why can't private buddhas just tell people what they did to achieve enlightenment
Because they themselves don't know. It's not like when you become enlightened you automatically understand what happened; the only necessary difference is that you no longer have any craving for anything. Actually understanding how you got there takes a much greater degree of wisdom.

It's much like having an epiphany - you realize something about your life, but you don't likely know what exactly you did to give rise to that realization.