Explain this quote in your own words. "frequently gave a 'false' impression of wisdom - one that did not rightfully represent the wisdom of the argument of its author."

My best interpretation of the quote would be that someone is deliberately misinterpreting someone else and twisting their words and meaning.

From the quote, "...a false impression of wisdom, that does not represent the argument of the author", it is quite clear that a person is deliberately acting unaware of the meaning of the words of a person or twisting the words and meanings.