I feel I made a cogent, reasoned point and topped it off with a forceful reproach.

Some people are more swayed by the former and others the latter.

What you call a "forceful reproach" is nothing more than name-calling. If your argument is convincing, you need add nothing more.

Emotional arguments are the only way to sway many people, everyone doesn't respond to logic.

That may be so, but the problem with that avenue is that often people think they've made a logical argument when it is full of value judgements. In this case the comment in question was full of value judgements and assumptions based on incomplete information (they may be true, but they may also not be), and the final appeal to emotion was nothing more than a strong emotional restatement of an argument that did not rest on logic to begin with.

If an argument doesn't resonate with you it's easy to simply say I respond to reason rather than emotion, or vise versa. Or point out the problems as you just did, perfectly fine approach, but you can't ban emotional arguments because sadly, most people are emotional, and those arguments tend to work better. It'd be nice if everyone only responded to non fallacious logical arguments, but it just isn't so.

Sure, emotional arguments are a vessel to deliver rational, logical conclusions to those who are not persuaded by logic itself. But rational conclusions and analysis come first.