In The Society of Mind, Marvin Minsky writes about "Intellectual Trauma":

One of Freud's conceptions was that the growth of many individuals is shaped by unsuspected fears that lurk in our unconscious minds. These powerful anxieties include the dread of punishment or injury or helplessness or, worst of all, the loss of the esteem of those to whom we are attached. Whether this is true or not, most psychologists who hold this view apply it only the the social realm, assuming that the world of intellect is too straightforward and impersonal to be involved with such feelings. But intellectual development can depend equally upon attachments to other persons and can be similarly involved with buried fear and dreads. [--] By itself, the failure to achieve a goal can cause anxiety. For example, surely every child must once have thought along this line:

Hmmmm. Ten is nearly eleven. And eleven is nearly twelve. So ten is nearly twelve. And so on. If I keep on reasoning this way, then ten must be nearly a hundred!

To an adult, this is just a stupid joke. But earlier in life, such an incident could have produced a crisis of self-confidence and helplessness. To put it in more grown-up terms, the child might think, "I can't see anything wrong with my reasoning--and yet it led to bad results. I merely used the obvious fact that if A is near B, and B is near C, then A must be near C. I see no way that could be wrong---so there must be something wrong with my mind." Whether or not we can recollect it, we must once have felt some distress at being made to sketch the nonexistent boundaries between the oceans and the seas; What was it like to first consider "Which came first, the chicken or the egg?" What came before the start of time; what lies beyond the edge of space? And what of sentences like "This statement is false," which can throw the mind into a spin? I don't know anyone who recalls such incidents and frightening. But then, as Freud might say, this very fact could be a hint that the area is subject to censorship

If people bear the scars of scary thoughts, why don't these lead, as our emotion-traumas are supposed to do, to phobias, compulsions, and the like? I suspect they do---but disguised in forms we don't perceive as pathological. [---]

This seems to fit the anecdote very well--your interlocutor could not find a fault in the reasoning, noticed it led to an absurdity, and decided that this intellectual area is dangerous, scary, and should be evacuated as soon as possible.