To take this example specifically ...
I regard such a remark as a sign of a lack of ability to communicate, or taking the time to communicate, or perhaps poor education. I might even feel sorry for the person who wrote it .. but probably not. Imo what needs to happen in response is not epithets but rather:
1. Identification of the logical fallacies of the statement(s) or argument If you do not or cannot explain the flaws in the logic of a claim or argument, then do not state that 'their logic is dumb'. Logic is not a matter of one's individual preferences but a fairly codified set of guidelines. For example: a straw man argument, or presuming the truth of a conclusion in one's premises (aka ' begging the question'). Logic is not about facts but about how we arrive at conclusions - the 'rules' of argument if you will.
All men are mortal
Alice is a man
Therefore: Alice is mortal.
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2. Carefully address statements you believe are wrong or false or misleading. IOW, fisk them. Fisking is a written argument where one person sequentially addresses each point of an of another person's argument.
Having done this then the peanut gallery will judge for themselves who or what is dumb.
The above is so much more entertaining and educational than exposing one's inability to communicate with cheap insults.
Edit: clean up sloppy syntax and spelling.