Imagine that someone you know has a reaction that you consider disproportionate to the severity of the event that caused it.

What you describe (someone's button's being pushed) is commonly known as a trigger. What they are experiencing might even be related to PTSD, though probably not in your example with the misplaced comb.

The idea is to keep up your rational arguments, to give them enough feedback

This may work in isolated cases, but most of the overreaction you describe is subconscious. Logic does not work well on the subconscious mind, if at all.

to actually learn the complicated thing that you're trying to teach them.

This often comes across as condescending and may easily cause resentment.