You can try to weasel out of it, but for all intents and purposes you did. Here is how you did it:

1. You compared the situation A to a hypothetical situation B, claiming it to be equivalent or comparable - A <=> B

2. You claim that someone describing the hypothetical situation as an overreacting description of the hypothetical situation - Describe (P, O (B)) => Insane (P)

3. By extension you imply that the person considering the first situation overreacting is also insane - Describe (P, O (A)) => I (P)

    (A <=> B, Describe (P, O (B)) => Insane (P))
      => (Describe (P, O (A)) => Insane (P)

Its probably unintentional as you did attempt to soothe it out (but that didn't help)

Personally I find that using the "understanding" method works much better than the "sootheing" method i.e.

"I understand why you think this way - <explanation of your understanding of the thought process of the other person> but you're wrong because <explanation where thought process goes wrong>"