Reid Hastings (Netflix founder) uses a different analogy. He compares a company as a high performing "sports team". With the idea being, you're working towards a collective goal. You each have you're own role. But if you're not performing, you get cut. Just like any athlete would get cut. The problem with the "family" analogy is it implies "unconditional love" regardless if you're messing up, failing, not performing.
The only reasons to have an analogy are you are 1) dealing with people who lack the acculturation to hold a professional job, or 2) you are trying to distort the notion of a company in your favor.