My fear of dogs brings involves a paradigmatic first-order desire: a desire to avoid the proximity of unsecured dogs. But a desire to avoid the proximity of unsecured dogs also motivates me to avoid activities that have a sufficiently high (which does not need to be high at all!) probability of leading to being in the proximity of unsecured dogs, activities such as walking to work. This, too, is a paradigmatic feature of this first-order desire.
But now one of the activities that would have a sufficiently high probability of leading to being in the proximity of unsecured dogs would be getting rid of my fear and hence desire for avoidance. If I didn't fear dogs, I wouldn't avoid the proximity of unsecured dogs. Thus, the desire to avoid the proximity of dogs motivates me to avoid getting rid of this very desire. But such motivation is paradigmatically the work of a second-order desire. Yet it comes about through exactly the same means-end reasoning by which the desire to avoid the proximity of unsecured dogs motivates me to avoid walking to work.
This isn't an exceptional case. Normally, the possession of a desire for A helps promote getting A. There could be exceptions: a desire to have many friends might not make one a good friend and joy might be the sort of thing that comes most when not pursued. But normally desires help promote what they are desires for—indeed, that's presumably at least a part of why we have desires. But then, when one reflects on this, the desire for A will motivate one to maintain a desire for A.
Fortunately, however, often the motivation to maintain a desire for A will not be as strong as the motivation for more direct means to A. This contingent fact makes it easier to rid ourselves of desires that we should not have: for even if the desire is very strong indeed, its motivational force for self-maintenance may not be all that strong, and hence we may be able to induce, through reflection on the perniciousness of that desire, a sufficiently strong motivation not to have that screwed-up desire. Notice, though, that at least sometimes that motivation-to-remove-desire will itself be simply a means-to-end motivation in light of a first-order goal. One doesn't want to die of lung cancer—so one works to remove the remove the desire to smoke.