When Jefferson says Americans "should declare the causes which impel them to the Separation," he means they should state to the world why they are forced to become independent. Why do you think he says that they should explain this to the whole world?

What comes with independence is the freedom to make your own decisions and do what you want without fear of restriction or consequences from some higher authority. If you make it clear to the world, you are declaring that no one can own you and tell you want to do or what rule you can follow.