It is fact.
Of course - people have egos and emotions, so when they hear someone tell them they are wrong, they will typically take that as criticism about themselves - and not the fact that you are disputing.
This is the complexity of language and communication, but in this case it's pretty clear. "You are wrong" is criticism on and aimed at the person.
However - if those details are provided, it is not personal, but just simply factual and shouldn't be considered an insult.
The other complexity is whether or not one is having a debate about something that can be factually quantified, versus something that is just an opinion.
If that means blunting objections as "that's incorrect" rather than "you're wrong", so be it. Two decades' experience, which is a tremendous run in online forum space, is quite difficult to argue with.
(Not that I don't occasionally argue with mods over guidelines, intent, and/or effects, not necessarily on this specific rule.)
If it is rainy near me, and clear skies near you, and I tell you the sky is grey, without corroboration from the weather report, I am wrong to you. If you say the sky is blue, without corroboration, you are wrong to me.
Gravity falls down. On Earth.
The boiling point is 100 degrees. Unless you're using Fahrenheit or Kelvin.
I find that when refuting people, instead of outright debasing their position with a right/wrong dichotomy, it works better to illuminate the possibility there is a larger breadth to the viewpoint. In this way, both views can generally share the same space. Healthily, if one can add such a descriptor.
This can be exhausting. When arguing product characteristics at work, I'm often tempted to say "that's terrible" or "nobody wants that". In my mind those would be factually correct based on my experience and understanding. But I still have to bite my tongue and remember the specific reasons those are bad ideas and "make a case". It is always received better with supporting information rather than presented as a fact. It helps me if I think of it as persuasion or education which is worth the extra time.
I think that would've been pretty clear from the post too, if you weren't so keen on giving a non-native speaker an English lesson ...
So you could use an LLM, privately, to soften people's opinions.
I just tried it for you, I won't copy it here cause the thread is about not using LLMs, but if you get too upset from somebody being simply direct and clear in their manner of speaking, the LLM is trained on enough American cultural baggage that it is very capable of softening that blow with the extra words you so dearly need to see past that red mist.
Someone might even be able to vibe code a browser plugin for it.
"They are wrong" is then valid, or "That is not correct" if I have misinterpreted them.