The argument that everyone has a philosophy is very straightforward:
To live, you have to act, and to act always involves a principle of action. Walking assumes the principle of gravity. Talking relies on the principles of intelligible sounds and coherent symbols for starters. All your activities are based on some kind of underlying principles, and principles are based on some kind of belief or knowledge. All beliefs and knowledge are based on some kind of specific philosophical point of view. Therefore , those viewpoints are the foundation of all your commitments.
This is why everyone has a philosophy.