Some clan of maquak (however it is spelt) monkeys have learnt to wash potatos in the sea water, making them salty while cleaning the sand off them (or something like that). This is a tribal only thing, and no other monkeys do it. It is assuredly taught to members of the tribe.
But to take this conversation down a new path: Instead of talking about all of the natural teachers (the parents, the tribal imparting of knowledge), I guess the first institutionalised teacher would be Socrates and the sophists... Socrates, and his intellectual progeny (plato, aristotle and many others) walked around leading philosophical discussions all their life. The sophists were people who were hired by the rish to teach all sorts of skills to them: Diplomacy, etiquette, ethics, governance etc.
I am sure there are many examples prior to these times in which stuff was taught (religion for example: Churches in whatever form) but this is the first thing I can think of, in recorded history, in which education has been organised to some extent within a society.