The family relationship has always been a horrible way of describing the employee/employer relationship. There's divorce or disowning someone, but do you really want to try and draw that comparison when you fire someone? A team has players and they're always being traded to different teams. That's both more positive and honest when you're trying to describe a high-performant culture.
And there's also no concept of unconditional love in a company. There's respect, which should be a given. But you shouldn't be expected to unconditionally love your co-workers.