It's a phrase that I've questioned for quite some time. It's easy and straight to the point, yes, but fails to look into the real reasons why one should 'fire fast'.
Firing fast for gross misconduct - i.e. excessive insubordination, theft, fighting, etc - is pretty much a no brainer, but firing fast for most other reasons, isn't. I'll tell you why: it often doesn't take into consideration the self reflection of a company on its own internal politics, policies, procedures, and even its static culture. Let me elaborate.
Certain internal politics will frustrate or cause employees to underperform if they are not provided sufficient mandate to do their job. These internal politics, if not policed or abolished by upper management, will also hamper the growth of a company, as quite often people involved in the political BS, are more worried about their own interests and not that of the company.
The same goes for policies and procedures. These should be audited regularly not just for if they're being done correctly, but also for efficiency and logic - do they still make sense how they're being done or can they be done differently or better?
Furthermore, often company cultures become static, always hiring the same type of people with not much diversity. Almost robots. Yes, it's important to have a strong culture within the company, but for example if a management culture of being 'too nice' i.e. not making people accountable for failing to meet their deadlines or completing projects is frustrating a new manager who's trying to improve things, then the company really needs to reflect internally!
Therefore as a company, first look at yourself before taking that step! Did you do everything in your power to make sure that your employee was given the right amount of guidance, tools, support and constructive feedback in order to perform at their best? Remember, they can't fix something if they don't know it's broken! Did you actually listen to them? Were there any early signals? Is it something that can be fixed with some coaching or a simple conversation? Is their negative performance a reflection of your company's shortcomings that you might need to reassess? Are you aware of some of the internal politics/dynamics and are some of those hampering the efforts of the company to grow?
You might be surprised to find some gold nuggets among them. I know from my experience I've had employees who I could have fired fast, but with proper guidance, communication and coaching, they eventually turned out to be quite amazing!