Why the Royal Navy has a strong claim to the longest continuous history

Which navy has the longest continuous institutional history?

The Royal Navy is the strongest candidate because its organization is conventionally dated to Henry VIII and has remained in continuous service.

The oldest naval tradition is different from the longest continuously operating institution. Other old candidates include Swedish and Mongolian examples, but they involve gaps or organizational changes. The Royal Navy's conventional institutional origin lies in Henry VIII's reign in the sixteenth century. Its continuity since then gives it the strongest claim in the terms used by the question.