Definition of Leadership

Lussier and Achua (2010) define leadership as "the influencing process of leaders and followers to achieve organisational objectives through change" (pg. 6).

This sounds all well and good, except for the 'and'. If both leaders and followers are influencing, then who are they influencing? Wouldn't the definition be more accurate to say that leaders are influencing followers? Obviously in human relationships it would be a two-way street, however isn't the purpose of leadership to have a leader exert more influence over a follower? Otherwise wouldn't the follower then become the leader?

It could be argued that the leaders and followers are influencing the organisation or those outside the organsiation, but then the problem still occurs then about who is a leader and who is a follower. If this were the case, then the organisation would by default become the leader while the external customers/consumers/clients would become the followers. This may be true, however it still does not define the role of those who are internal to the organisation whose jobs it is to make decisions and provide direction for the others within the organisation.

My amended definition is "the influencing process of leaders over followers to achieve organisational objectives through change".
 
Reference
Lussier, R. N., & Achua, C. F. (2010). Leadership: Theory, Application, & Skill Development (4th edn.). Eagan, Minnesota: Thompson, South-Western.