In a public forum, maybe to convince others who won't be taken in by the pigeons "struting". Your refusal to argue on the basis that they're too "dumb" to play the game, on the other hand, will be much more damaging to your position.
Trying to convince one single individual of something is a mugs game anyway, you can only "sow the seeds." Even if they seem change their mind, they probably only do so to appease you in that moment.
It's very unlikely you'll change another's POV, regardless of their intellect, whereas arguing in front of others, including online, is a very good way of convincing other people, witnesses, of your view.
Even if such a person does not follow your points well, such an interaction can have a benefit to you.
Mark Twains quote about not arguing with people who drag you down to their level and beat you with experience (I'm butchering that quote a little bit) is admittedly relevant here and bias will always exist in the minds of all people even the most rigorous, which is why the market place of ideas has flaws but possibly the worst thing you can do is to refuse an argument on the grounds that they are some kind of name you have designated to them.
In the case above that name is "dumb". Even though that post was probably an attempt at humour, the point still remains, in the minds of those you would like to convince, I.e. Not people who already share your views (that is an echo chamber), you will be perceived as the inferior of the two parties. If you resort to name calling of any sort and refuse argument, your views will take hits for this (why would you not defend your views if a person's misunderstanding of them is "dumb"? Looks like you "can't" defend them.)
Remember kids, whether we like it or not; optics are important. The art of rhetoric has been used for centuries by unscrupulous folks to trick people into certain views, sometimes these have been conscious tricks, sometimes unconscious on the part of the speaker (for instance, it's easy to fool yourself with the use of logical fallacies).
This is why it is important for a person who does not wish to fool people or obfuscate to also present their arguments with good optics. Simply refusing an argument with an "unworthy" opponent because they're "bad people" or "unintelligent" and therefore will not change their mind and use their experience of ignorance to obfuscate, willingly or not is actually bad optics on your part.
First of all, value judgements don't often move witnesses of your conversation. You may be trying to convince them of your values, even in that case you must provide a reason why they should follow. Secondly highly judgemental views towards an individual such as they are "dumb" will also, in most cases, look bad on your part, unless you are arguing against somebody extremely obnoxious and ignorant but it rare, on the Internet, to find non-troll who will be this extreme.
Sure in some instances name calling can have a positive impact. For instance, H.L. Mencken once wrote, what is regarded by some as the greatest anti-religious polemic of all time, that all those who believed what methodists were telling them were not being fooled but rather that they are fools. Notice though how this was against a group of people holding a belief and not against an individual in mid-argument. Name calling often fails in that context.
All of the above doesn't merely have to apply to high end arguments about philosophical or political views. For instance if you are a customer in a dispute with a company and the worker who is disputing your claim is "rude" or "dumb" these same rules apply in an argument such as that. It also works from the workers perspective. People witnessing your dispute will have more consideration for your side of the argument, if you don't act superior or resort to name calling thus refusing to speak further.
Lastly, maybe you're not trying to convince anyone of anything, however one has to wonder why you would want to consider arguing any points in the first place. The only conceivable view (aside from just liking to argue) is that you wish to signal your virtue to those who share your opinions, which all in all is a very self-serving approach, not a respectable one and if you want to actually see change in the world, not a useful one.
