This isn’t really true in general: You can post all the links you want on most social media, though there are tenuous theories that including links will get you less promotion on certain platforms.
What is very true is that most social media users don’t like to click on links. They read the headline, look at the included image (if any), and assume they understand the whole story from that context. They jump to the discussion to comment about it or see what others are saying without leaving the site.
For people who just want to scroll and see a lot of different things, leaving the site to go in depth on 1 or 2 links doesn’t really fit their preferred social media operating style.
This holds even on sites like Reddit or HN, where you can some times jump into a comment section and immediately recognize that half the commenters haven’t read the article at all.