Readers that have spent time bored on the internet will have come across circumstances where a complex, difficult to understand principle has been co-opted in order to substantiate some utterly ridiculous philosophy desperate for validation. Who hasn't seen Heisenberg's uncertainty principle used as "evidence" for the existence of god or as "proof" of some other soft belief? We're well familiar with the often-misunderstood worlds of banking and finance used as a structure to endorse a belief in a Jewish conspiracy or the complicated world of politics to enhance some notion that the world is being run by Free Masons, Aliens or whatever other group can be called upon to spread fear and distrust among the ignorant. This sort of thing has been going on a long time: the ancient Greeks identified practitioners as sophists, who charged money to dupes in order to give them an "education" that was something less than that.
Just now, gamers will have encountered a familiar argument that because role-play is complicated and full of humans speaking and "fostering a story," the actual process of role-playing can only be described as gray "flexibility," far too complicated to be understood and certainly defying a rule-set that can account for all the possible contingencies that will arise. Therefore, a DM must, must absolutely, so much so that it cannot be disputed, be "occasionally" arbitrary. That is to say, actually arbitrary, since only the arbitrary dictator can decide when arbitrariness is necessary.
We often fail to recognize the importance of communication in role-playing and far-too-often we half-ass a player's contribution (not in my world, as I'm a hard-ass). If a baseball umpire suddenly stopped calling balls "strikes" and began calling, "Swing and a miss, One! Didn't bother to swing at all, Two!", the players would understandably stop and ask what the fuck was going on. But if a player at a role-playing campaign suddenly started referring to "hit points" as "meat status," chances are the other players would laugh, then start using it themselves, then carry on with it every once in a while because "fun." Because who gives a shit? Means the same thing.
This is where the sophists jump in. Because many games are run without the least effort towards creating structure or demanding consistency, and because many of these games are presented as "fun," a word that in no way describes a consistent, universal experience, this is argued as "proof" that the only way to control players is through arbitrary control and flexibility.
In keeping with the videos I've been relaying just recently, what is "flexibility"? It sounds like an important word, something that a DM has to be, but it is often used as an extremely fluid term that could describe, well, anything. How can one be both "flexible" and "arbitrary" at the same time? Like in the xkcd comic above, the word is being redefined for the sake of sounding like something positive, while utterly ignoring the word's actual meaning.
To be flexible [definition 1] is to be capable of bending without breaking. In a game sense, to carry out the rules as written with some understanding that unheard precedents need to be ruled upon according to principles that support the sentiment and virtue of the game, not the individual. If a ruling is made that breaks trust and causes others to question the legitimacy of the DM, then rules in place up to that ruling have been broken and flexibility has not been the result.
Again, to be flexible [definition 2] is to be easily modified to respond to altered circumstances and conditions. In the game sense, this means to respond to outside circumstances, meaning that the player's actions and choices should be respected, enabling an open-ended, variable and adaptable experience for all concerned. I've been describing this lately, where I've said the world has to have features that adjust as the players adjust, that respond to manipulation without commanding or stultifying that manipulation. This does not mean that breaking the rules is suddenly okay ~ the first definition still holds ~ but it does mean that the DM's actions cannot arbitrarily counteract the player's behaviour. This would be the equivalent of a car's steering wheel suddenly locking up without explanation ~ something that no driver wants, ever.
Finally, to be flexible [definition 3] is to be ready and able to change so as to adapt to different circumstances. This sounds like definition 2, but in this case it applies to the person and not the situation. It means that a flexible DM doesn't want to be arbitrary, doesn't want to be intractable or intolerant. A DM needs to want the players to want the game to be plastic in its design.
Every time a DM sets out to be arbitrary, to make a random choice on a personal whim, rather than according to any reason or system, unrestrained and autocratic in the use of authority, the DM has specifically not been flexible. Yet the sophist would have you believe that the "truth" about gaming is found in the "gray space" between flexibility and arbitrary decision-making.
This is like saying that the effectiveness of a car is in the "gray space" between the car working as desired and the car randomly breaking down. There's nothing gray about it. We know why cars break, though they may be complicated; and even the least little bit of investigation by a player will ascertain almost immediately why a campaign doesn't work.
Because the DM is a dick. And thinks that's acceptable. Because role-playing games are complicated, and arbitrarily is the only way they can be run in order to maintain momentum, story, interest, fun . . . you know. Reasons.