As I understood it from a previous incarnation of this topic where it involved Google it’s less nonsensical than it sounds (at least it was in that specific case, this one may be different, so take this post with a grain of salt).
The thing these media companies have issue with is that their content is displayed on the social media website’s feed, usually in the form of a headline and a short summary. Many people will only read the headline and this summary and will never actually visit the website of the media company, so they can’t monetize these users through the ads on their website or through subscription services. Meanwhile Google/Facebook get to extract value from their content for free.
Of course by that logic you could maybe also say that users should get paid for posting links as they have added their own value by curating the content displayed on the social media site, but they don’t have a team of lobbyists. :)