tl;dr it's a stupid CEO fad that says if you tell your employees "We're a family" enough times they'll feel too guilty to quit until you decide to fire them and offshore their jobs.
FYI if anyone at your company says "we're a family!" get your resume polished up.
edit I recall reading a story about a CEO who found once his company expanded beyond 150 people the culture fell apart and people became disinterested and detached from one another. So he broke his company up into 100-150 people groups to keep them closer-knit. Something about being related to ancestral human settlements being around 150 people.
tl;dr it's a stupid CEO fad that says if you tell your employees "We're a family" enough times they'll feel too guilty to quit until you decide to fire them and offshore their jobs.
FYI if anyone at your company says "we're a family!" get your resume polished up.