Reactionary is a pejorative usually used by Marxists, and implies drawing one side into their false us-vs-them dichotomy where the "them" has a "fair game doctrine" applied to them. Usually other epithets soon follow: racist, criminal, etc.

Not only is it not, as you note, an argument, it's a pejorative label designed to discount and demonize the opponent. It's also likely to be used by someone in a political cult (or "high demand new political movement" if you prefer).

George Orwell had a really fun article on "Politics and the English Language" which goes into some detail on the controlling nature of such language and the people who use it.