Ok I didn't mean literal family. I also think most people who write blog posts talking about family mean "our team is like family"? I have many people who are like family that I have worked with in the past.
Ok, from context it sounded like literal family so I was confused.
Still, I don’t think “work is not your family” is antagonistic and I don’t think it implies you can’t form meaningful relationships with your coworkers. I interpret it from the other direction more like “don’t expect your coworkers to be your family”.