Sometimes, and I don't think I'm the only one who does this, I present what I regard as a clearly mistaken or otherwise flawed formulation of a doctrine or argument in order to demonstrate (or allow the students to demonstrate) what is wrong with it. There are a couple of reasons. For one thing, philosophers can be very persnickety about formulating doctrines and arguments in highly specific ways, and this helps to explain why: if you formulate the doctrine in a careless manner, your doctrine (as formulated) will be susceptible to trivial or insubstantial objections that show the particular sentence to be false without touching the heart of the theory. I often do this to justify a use of a (somewhat) inelegant formulation when there is a clear alternative that is more elegant but which has silly consequences.
It can also serve as an interesting lesson in the history of ideas. If the mistaken formulation is taken from a historical source, it can help the students to get a feel for the history of an idea, and to see how the idea has evolved and changed over time, (hopefully) becoming more sophisticated and awesome.
But I have started to worry that this technique is counterproductive, because some students, once exposed to a mistaken formulation, can never be convinced to let go of it. These students walk away from the discussion thinking that (I have taught them that) principle X or theory Y or argument Z is this garbled or self-contradictory piece of garbage, when the point was supposed to be "it's not that piece of garbage, its this piece of awesome, and here's why." And so the worry is that presenting instructive mistakes is unnecessarily confusing to (some) students, which seems to me to constitute a prima facie reason not to do it.
But it also seems to me that it is unlikely that careful and conscientious students will fall victim to this kind of confusion; and that such a student might well benefit from instructive mistakes; and that if that's true then this sort of thing might make a useful diagnostic tool; and that it is not possible to remove all potential sources of confusion from a philosophy class; and that I am probably overthinking this the way I overthink everything.