The stimulus presents us with a conditional statement. In this conditional statement there are two necessary conditions and one sufficient condition. Let's examine how we break this down into a diagram and then see how E must be false.
"Only if" introduces necessary conditions. Two were provided. Only if people are convinced that their efforts are necessary and that with the expenditure of these efforts, achieving the goal is possible. These are necessary conditions for people following a leader. Which is the sufficient condition.
Follow Leader - > Person feels necessary AND thinks goal is achievable
Contrapositive:
NOT person feels necessary OR NOT thinks goal is achievable - > NOT follow leader
Answer choice E triggers the contrapositive (NOT person feels necessary) and proceeds to say that some of these people will follow the leader. But, using our diagram, we clearly see that all who do not feel necessary, do not follow.
Hope this helps. Please let me know if you have any other questions.