Stan, I do absolutely agree with you, but nonetheless I take part in online discussions from time to time. Maybe it's really just my guilty pleasure, but I justify it be saying that there might be an undecided reader whom I have to convince with my superior arguments ;)
Hate to say it, but the label of the x-axis doesn't make any sense. Moreover, should this really be a line graph: these are discrete classes of disagreement, not a continuum of underlying parametric data (ie. what does it mean to be halfway between these two conditions?) — surely a barchart would be more appropriate. So, the x-axis would be labelled "basis of disagreement", the first low column would be "nature of reality" (though "verisimilitudinousness" sounds better to me) and the high column would be "means and form in which an idea is expressed."
I see argument over terminology as usually a face-saving tactic. It is what someone those who hate to admit personal error fall back to when the alternative is an admission of personal error – or an admission that the discussion so far has been completely pointless.
There are cases when it is used otherwise, but even in such cases I rarely consider it important enough to discuss beyond a single message or so.
This is especially true on Twitter. They bruise their enemies, but they eat their own. And usually the fall from grace or the execution involves the use or abuse of jargon. It bears a startling resemblance to the Moscow Show Trials, in 140-character bursts.
Isn't there a somewhat different but common phenomenon where a purely terminological criticism seems to be a passive-aggressive proxy for substantive disagreement that the critic cannot be bothered to spell out explicitly? Sometimes a comment along the lines of of "your original post used the word 'handicapped' which is hurtful and insensitive; you should say 'disabled' instead" does mean "I concur with your substantive point but want to encourage you to express it differently so you don't needlessly alienate people who might be inclined to agree with you" but other times it means "your use of insensitive terminology is sufficient evidence that your substantive claim is wrong that I don't need to offer any further counterargument."
If someone changes their mind on the spot, they didn't care about the subject, or are just telling you what you want to hear. If you're a salesman, for instance, a great way to build confidence is to disagree with your mark about some irrelevant issue and then be convinced by their brilliant reasoning.
That said, people do change their minds due to arguments, just usually not until later and not solely because of that discussion.
In biology especially, people really *do* argue over terminology (for groups of organisms, genes, etc.) and some people will make a point of going out of their way to not use terms coined by rival groups even after they've become standard usages by everyone else.