Clicking “Share” on someone’s Facebook status is a lot easier than doing a “copy and paste”, but the Share button has limitations. The biggest restriction is the original user’s privacy settings. According to Facebook, if someone’s setting says the post can only be seen by their friends, then sharing the post will only show the content to your mutual friends. Sharing is largely only effective if the original post is on a public setting that lets anyone see it, regardless of whether or not they are friends with the original poster.
So when users call for people to “copy and paste” but not “share”, it is to ensure privacy settings are not preventing a message from being spread. If the goal is to get a piece of information to reach the largest potential audience, then copy and paste is the safest best.