"straw man argument" is correct and usable in written English.
You can use it when referring to when someone presents an argument that is not accurate or complete, and then attempts to refute it. For example: "He used a straw man argument to try and prove his point, but he had not considered all of the facts".
That is a straw man argument offered by both extremes.
But again, this is a straw man argument.
Yet this is a straw man argument if ever there was one.
This straw man argument is a historic staple of rightwing, anti-equality arguments; the only problem is that no leftwing thinker has advocated literal equality of outcome.
He then flawlessly attacks a straw man argument about socialism that no Democratic candidate has ever made in history: "they want to be involved in every aspect of [people's] lives.
The policies of those who claim to care for nothing more than protecting human life are a straw man argument to prevent women from exercising their right to bodily autonomy and participating fully in social, economic, and democratic life.
And scientists have an inconvenient habit of not being diverted by "straw man" arguments.
A little reading will serve to show that climate change deniers are almost always starting by setting up classic straw man arguments (as in the article Gary linked to) which are not in fact the scientific argument.
He urges the big chains to be pro-active in changing Americans' diets and in helping consumers to make better choices: "The restaurant industry makes a number of false, straw man arguments.
Representative Paul D. Ryan of Wisconsin, the party's vice-presidential nominee last year, said Mr. Obama had used "straw man arguments" in taking an implicit swipe at Mr. Ryan when he said that programs like Medicare and Social Security "do not make us a nation of takers; they free us to take risks that make this country great".
Big businesses and the federal Treasury are setting up "straw man" arguments against a tougher crackdown on multinational tax avoidance, the Tax Justice Network says, advocating Labor's policy as "just the beginning" of sweeping changes that would force companies to pay fair rates of tax in Australia.
