In which direction to use words as Leadership and Cooperation

Perhaps think about it this way...

Everything you've learned about leadership shouldn't be used externally, but internally.

And that leader should learn to cooperate well with everyone outside you.

confused people

But if you're internally just cooperating, you will never effectively lead anything outside yourself.

That you know something, and can use something well, doesnt yet mean you're doing it right.

And that applies especially to words like leadership and cooperation.