Now, nobody exactly knows where this quote originated, some say, it came from Bob Smith, while others say from Mark Twain, although Mark Twain's quotation is slightly different from the one above.
But knowing who said this quote is not the point of bringing this topic here. The reason is that the quote is reasonably sound despite the fact that it sounds like an Ad Hominem.
BTW, what is an Ad Hominem?
An ad hominem is latin for "to the man" or "to the person". It is an attempt to negate the truth of a claim by pointing out a negative characteristic or belief of the person supporting it. It is normally described as a logical fallacy, in other words, it is a false statement.
Well, if you look and carefully analyze the quote, the word "Idiot" there may sound like an Ad Hominem, raising the argument "How would you know that the person you are referring to with this quote is an idiot, if you haven't even argued with him?" If that's the stance, then the quote would be rendered false, however, it is not the case. The quote itself was referring to an already verified idiot, although, idiot as a word that may already be too much, but it holds true for people who never learn or never accepts their mistake.
Of course, arguing is OK, it is a process of checking the logical consistency of an argument. However, arguing is only helpful when it is constructive for it provides a solution to a conflict at hand, otherwise, it's a complete waste of time, most especially if you are arguing with people who insist their ideas or opinions to be correct when it is already proven wrong. But, how would you know if a person is wrong? Well, that's another question and a good one. One of the means to determine the correctness of an argument is to rely on proof (strong evidence), the others are determined by its consistency with reason. If it is unreasonable (often hitting logical fallacies), then it's wrong.
So the quote "Do not argue with an idiot. He will drag you down to his level and beat you with experience" may only apply to an idiot, but never on those who can argue and defend their constructs well. It is a good quote, and quite reasonable.