The implications of the government’s demands are chilling. If the government can use the All Writs Act to make it easier to unlock your iPhone, it would have the power to reach into anyone’s device to capture their data. The government could extend this breach of privacy and demand that Apple build surveillance software to intercept your messages, access your health records or financial data, track your location, or even access your phone’s microphone or camera without your knowledge.
Cook is explaining what exactly an encryption by Apple would mean to millions of Americans, and even international Apple customers. This violates laws of privacy, and would mean increased surveillance and government understanding of our whereabouts at all times. This is important because Cook is educating his audience, particularly Americans, as to why they're publicly denying assistance with a terrorism. Cook is seeing the bigger picture here, and is asking his fellow Americans to do the same.
I can see myself using this source in the future to include Apple's side of why they're not including themselves within the case, directly from the CEO. Cook provides evidence for his claim, and it allows for sympathy from his audience.