Why do people use the word anarchy to describe chaos?
They don't similarly misuse related words. Monarchy is always used to describe a structure of authority, as are oligarchy, plutarchy, and whatever other -archy there might be. But anarchy is not only used most often as a synonym for chaos, it is almost never used to specify a structure of authority; even worse, it seems to be the preferred term for chaos. Why is this?
The Progressive Ernest Partridge provides two quotes that are on target. The first is his own:
Language is the constant yet unnoticed current that carries our thoughts. Thus, in the game of politics, the party which controls the language, controls the contest.
We used to see this back when even non-Christians in the US considered themselves Christians. When someone who had come to repentance, pledged his allegiance to Jesus, been baptized, and become a church member would tell someone who had done none of these that the latter was not a Christian, the response would often be anger because the two would be using Christian to mean two different things. The latter would use the word to mean "a good, respectable person," and so when the former would say, "You need to repent and follow Jesus to be a Christian," the latter would say, "But I am a Christian, and I resent you implying that I'm not." So those who used Christian to mean what only that word means were hard pressed to communicate what they meant, and that was before beginning to deal with the natural human resistance to the gospel message as properly understood.
Also, people respond from the heart, not from the brain. Advertisers "don't sell the steak, [they] sell the sizzle." They don't sell the product, they sell the image that the buyer will have in his mind of himself when he buys the product: handsome, masculine, feminine, popular, nonconformist, healthy, or socially responsible. We are emotional beings: emotions are so called because they are what sets us in motion.
If he who controls the language controls the contest, and the way to influence people is through their emotions, I would suggest that those who purposely use anarchy instead of chaos to describe chaos are people with vested interests in maintaining the power structure, either because they are now in power or because they expect to be in power someday, want to give anarchy a bad name. This has two benefits for them: it provokes a knee-jerk reaction against people who call themselves anarchists, and it leaves us without a graceful self-appellation. Reasoned conversation ends before it begins.
Partridge again, quoting George Orwell:
The purpose of Newspeak was not only to provide a medium of expression for the [Party's] world-view and mental habits ... , but to make all other modes of thought impossible. It was intended that when Newspeak had been adopted once and for all and Oldspeak forgotten, a heretical thought - that is, a thought diverging from the principles of [the Party] - should be literally unthinkable, at least so far as thought is dependent on words. Its vocabulary was so constructed as to give exact and often very subtle expression to every meaning that a Party member could properly wish to express, while excluding all other meanings and also the possibility of arriving at them by indirect methods. This was done partly by the invention of new words, but chiefly by eliminating undesirable words, and by stripping such words as remained of unorthodox meanings... Newspeak was designed not to extend but to diminish the range of thought...
(To be fair, another possibility is that someone used the term as metonymy, like saying "the throne" when referring to the king, and it has simply become a cliché.)
If the two words are truly synonymous, wouldn't one be redundant and fall out of favor? Why would the preferred term be the less etymologically defensible? The most logical reason is that someone wants to take away every means we have of expressing ourselves and thus capture the loyalty of those who don't think for themselves without allowing us to put up a serious fight.
Jesus calls his people to become humble and harmless like little children and doves, to serve our neighbors, and to be known for our gentleness. Human nature makes obeying that call difficult enough under any conditions; for those who consider themselves above their neighbors—archons—it is all but impossible. Only anarchy provides natural rewards, and thus incentives, for Christian obedience.
On that basis, I would say that the mind behind the confusion of anarchy with chaos is that of the enemy of our souls.