If you can respond to these criticisms, you've been paying attention this term.
1. There is nothing to study. Mystics have private experiences, and by their own admission communicate them badly. It is like studying UFO sightings. It leads to speculation about fanciful stories that have no hope of corroboration.
2. The supposed "reality" that the mystic accesses could just be the affectation of a psychotic mind. There is no way to tell the difference between delusion and mystical experience.
3. Mystics tend to challenge order -- in philosophy, theology, government, morality. They are therefore divisive and destructive to all normal functioning. Studying this is anti-social.
4. Mysticism adds nothing to the social world. A "moral mystic" is almost an oxymoron, because mystics are solitary, while morality is public. This solitary nature can lead to quietism. Furthermore, the other-worldly orientation of most mystics devalues the world. The material world is just a world of appearances, and so can safely be dismissed.
5. Mystics do bad philosophy. There are no arguments, rarely any reference to the philosophical tradition. Mysticism is not rational -- to accept the mystic's version of the world, you have to have the mystical experience. Furthermore, mystics may only have a rationality within their own system, but they are often quick to use rationality to condemn others.
6. There is no ultimate value in the mystical insights, apart from having the experience. It is a little like getting high on drugs -- fine for the one taking drugs (unless of course they overdose), but of no value past the momentary "hit".
7. Mysticism makes for bad theology. You can get a 2-tiered system -- those that have had the mystical experience (the elite) and those who have not (the herd). This can lead to a situation in which the mystic can abuse the experience, gather power for him- or herself. You can ultimately end up with David Koresh or the Solar Temple Cult.
8. Further on this point, mysticism can lead to intolerance. After all, why would the mystic have to take anyone else's experience into account if he or she has seen true reality? Or, if it is not intolerance, the mystical experience at least can lead to a patronizing attitude to those who have not been properly illumined.
9. Anything worthwhile that a mystic has said, has been said better by a philosopher. This is true because philosophers do not appeal to private experience.
10. Mysticism can lead to an abandonment of self. The mystic can lose him/herself in the Other. It is a suicide of the person, if not the body. It is irrational to pursue this.
11. The study of mysticism will not lead to mystical experience any more than philosophy of religion will lead to faith. So, even if we think that mystical experience is a good thing (despite all the objections already raised), studying it might still be a waste of time. In fact, studying it may actually do violence to it, since the mystical experience is supposed to go beyond all attempts at rationalization.