I'd strongly recommend against directly assuming something to be counter-persuasive i.e. don't say "the use of such language incites backlash against the author" or "readers will not be persuaded by such ideas". This is the same idea as not directly assuming that they definitely will persuade the reader, i.e. don't write "the reader is definitely persuaded" or "the reader will support the author" but rather write "likely to support" so qualify your statements.
In terms of counterproductive techniques, I would frame it in the context of how it would persuade some but not all, as I don't think someone is that stupid to contradict themselves unless for a reason. So either point out that reason "the author employs such use of seemingly contradictory sensationalist evidence to highlight..." or say how it may persuade and may not "while some may be persuaded by this rhetorical language" others upon deeper analysis may see through this tactic..." But only 1 or 2 sentences max. Don't drag the point as you don't want to make out that you think the author is an idiot - after all they're writing the media piece published in a newspaper - you're writing a flimsy language analysis for school. Which one's more credible?
Overall I would avoid it. I don't like it. But do it if you must in the ways I've pointed out.