I agree with your basic point that the author’s dismissal of the man’s request for a logical discussion as normative is frustrating.
I think your point would be better served, though, if your own response didn’t have so many hallmarks of an emotional argument (use of sarcasm, calling the author lazy, etc.) — although it does provide a good example of how emotional responses can derail a conversation. Note how Dehlilia Cooper’s response continues in this same vein; rather than simply debating the merits of logic-based conversation, she ends by calling you smarmy and cold, and doesn’t seem to be at all swayed by your argument — even though you made plenty of good points.
I think what people misunderstand is that, keeping your emotions at bay in a conversation does not mean that the conversation is not informed by emotion.
The difference is, in a so-called ‘emotional’ conversation, people tend to yell or cry or exaggerate, and all of these things serve to put the other person on the defensive, or to poke holes in the little inconsistencies in the first person’s argument, rather than focusing on where they can agree. But in an ‘emotionally informed calm’ conversation, each person does their best to express themselves in a way that helps the others to see their point of view without putting the others on the defensive. You could think of it as being ‘nice’, but that’s not really the point. The point is that people have a hard time hearing things clearly if it makes them a target — so rather than yelling or crying at them, it is in the speaker’s own interest to make listeners feel comfortable so that they will be better able to hear what the speaker is saying.
I’ll end by saying that the ‘emotionally informed calm’ conversation is not normative. It is rare, and I think it would help everyone a lot if way gave it more of a chance.