There are three things I don't like about that argument.

1. The idea that small excerpts of copyrighted works are fair use that don't require licensing or payment is also widely-used in journalism.
2. At least in the case of Facebook, publishers get to decide what's in the previews using open graph tags.
3. News organizations have not lobbied for general changes to fair use, but special legal status for themselves and a few tech companies. Laws centered around special status rather than broad principles tend not to work out well in the long term.