Consider a Stackelberg game (i.e. one which fulfills the requirements described above for sustaining a Stackelberg equilibrium) in which, for some reason, the leader believes that whatever action it takes, the follower will choose a Cournot quantity (perhaps the leader believes that the follower is irrational). If the leader played a Stackelberg action, (it believes) that the follower will play Cournot. Hence it is non-optimal for the leader to play Stackelberg. In fact, its best response (by the definition of Cournot equilibrium) is to play Cournot quantity. Once it has done this, the best response of the follower is to play Cournot.