The "united" part was to prevent large, external states (initially, Great Britain) from taking away the liberty of each small state to live as its own citizens

The "united" part was to prevent large, external states (initially, Great Britain) from taking away the liberty of each small state to live as its own citizens chose to live. The US Constitution was a mutual-defense pact meant to defend that liberty while, at the same time, defending the states from similar threats from one another. Most things in life would be state-based, where the citizens lived. Federal things were for state vs state, both internal and external, not state vs citizen. The point of it was to defend the independence of small groups against the large. When local opinions changed about the "right" way to live, which history shows happens again and again, this system allowed the local group to change how they lived without requiring the "permission" of other states (internal to the union or external). If your own group (or you) changed, and you no longer liked your local state as much as some other where they made "better" choices, you would have the option to vote with your feet, as hundreds of millions have over the centuries. This system also attracted vast numbers of people from other places who chose not the "country" but the specific state that most suited them.