In order to be a successful trainer, leadership qualities are essential. The trainer needs to direct the learning experience of the trainees to achieve the desired learning outcomes, without letting the class slip into chaos. Also, the trainer needs to infuse energy into the class so as to create a learning transformation. Learning is a change process. Any change requires energy. In training, this energy (almost always) comes from the trainer. Thus a trainer has to provide energy and direction. This is exactly what a leader must do in order to get his team achieve the required goals.
In addition to providing energy and direction, a common requirement for both teachers and leaders is strong communication skills. Just as a trainer must know how to deliver his/her subject matter in a manner that is clear to the audience, a leader should be capable of articulating his/her vision and delivering the message.
So it is not surprising that several famous leaders and celebrities were teachers. The former President of the USA, Lyndon Johnson was a teacher, as was Benito Mussolini – former Italian dictator (bad example probably, but you get the idea!). And it is also unsurprising that many great leaders chose to spend their post-leadership years in teaching.
A couple of interesting articles in this line of thought: