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I agree. I'm not saying that this form can't be used as a means of examining our intuitions. For example, "meat is murder" is a snappier way of asking "Why, given that we're so worried about harming humans, are we so callous about harming animals?"
But then once the other person answers you with something like "It's because animals have no natural rights" or "Because animals don't have sophisticated enough nervous systems to suffer" or whatever it is they say, the debate has to shift to whether or not that objection is valid. So "but meat is murder!" shouldn't be used as a counterargument to "Animals don't have sophisticated enough nervous systems to suffer", because this latter statement is already answering the question the former was intended to ask.
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I don't think it's precisely about mindless repetition. For example:
A: I think eating meat is morally okay, because animals have simple nervous systems and can't feel pain.
B: But meat is murder!
Here even though A spoke first and there is no repetition involved, I still think B's response is inadequate, because B is accusing A of double standards after A has explained the double standard away. The reason why this is more dangerous than (if not worse than) "If the glove won't fit, you must acquit" is that B looks like she is making a novel and nontrivial point and it's not immediately obvious that this is a non-argument already addressed by A's statement (whereas hopefully no one takes the glove argument seriously as an argument)
Again, the objection seems to be more about the particular USE of the argument than the nature of the argument itself (what I call above "non-responsiveness"). I would genuinely like to understand why analogies of the kind you call the Worst Argument in the World are so harmful (and I appreciate your engaging on it). Is it your claim that people are particularly likely to take analogies seriously as arguments, more than other arguments? Is it their very power that makes them so bad?
Rhyming and other poetic tricks, like showing a picture, make statements feel more true to hearers; are those tricks less dangerous than analogy because we (think we) are immune to them? I can kind of intuitively understand what you mean by something being a real argument or not ("as an argument"), but I'm not sure why things taken seriously as arguments are more dangerous than sneaky, non-argument cues that make things seem true.
I wonder if what you really want to destroy are "things effectively masquerading as arguments that aren't really arguments." That class is not exhausted by inexact analogies (which is to say all analogies), nor are all inexact analogies members of that class.
I think metonymy (association, like eugenics --> Hitler) is a much more harmful cognitive sin than metaphor (which at least requires a theory of why things are similar).