Back in the day, when I was at school in the Sixth Form, we had to do General Studies. Part of the course was to analyse how different newspapers covered the same story and to be aware of bias. In those days (1971-1973) the newspapers were far less 'sensational' than they are now and journalists did their own work rather than relying on feeds.
I'd love to do a course on the same subject today (maybe keep an eye on FutureLearn offerings), because the birth of the internet and mobile technology has changed the way the public receives its media. Before the internet, groups with an agenda had to rely on physical leaflets, but these days it's so easy to get into everybody's living room across most of the world.
I think everybody should be aware of bias and, of course, it's in every piece of writing - even what I'm writing now. I see so many ideas being 'recycled', often word for word. It's so easy for an effective writer to get a message across. There is loads of research on the vocabulary needed to understand various newpapers (and internet articles) and the kind of techniques used to persuade. I think it should be part of English Language in schools and is much more useful than teaching about subordinating conjunctions.