I'd agree that "family" implies you're going to put the relationship itself over most rational reasons, and businesses can't do that. If you want to say they're family then the business should also plan for a pension that all employees get or something similar - otherwise it's just a tactic to manipulate people

Of course you treat family members well when they "deliver" for you, the real part is when they can't deliver and you still support them.

No one should use "family" at work, it's as the other commenter put, creepy. You can treat people with respect and trust without taking on a para-familial relationship with them, that's super inappropriate and exploitative (although sadly all too common).

>I agree that the "family" metaphor breaks down around termination

It breaks down the second you actually compare your family to your company. I think that basically every single person would do many, many things for members of his family that he wouldn't do for the members of his company.