I will agree with you that a short response simply stating that "you are wrong" is aimed at the person - if it isn't supported with the facts, resources and details about why they are wrong.

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.