To state that teaching is needed in order for a student to be educated, seems very broad of a statement to make. In order for one to teach there needs to be another person there to be taught, which brings up many extraneous issues in regards to the intentionality of both of these subjects. If teaching were to imply education then it would entail that learning takes place every time teaching occurs, and this simply does not exist.
I would like to argue that there is however a direct correlation between education and learning. If you think about it without learning there can be no education given that to learn is to understand the concepts within education. I believe that education and learning are so interconnected that education could not exist without learning. The learning that is associated with education can not be conditioned, which is an essential element that tends to be associated with teaching. It is obvious that there is a logical connection between education and teaching, however it is the concept of learning that seems to separate a positive correlation between the two. Teaching may simply be an activity designed to bring about learning amongst a world where people learn something new everyday, without having to be intentionally taught by another.
Just something to think about!