It's about giving power back to the states, and in turn the people. So a state and its people would have the power to decide on something like abortion rather than a single centralized leviathan-authority.
> power back to the states, and in turn the people
That sounds quite Stalinist. The people are not the state.
> So a state and its people would have the power to decide on something like abortion rather than a single centralized leviathan-authority.
Right, so your federal government is a centralised Hobbesian leviathan, but state government is not? How is state government not centralised? It's just centralised at a different level.
You know what would not be centralised? Allowing individuals bodily autonomy. Let them decide whether they want an abortion, not have them be forced to carry foetuses to term against their will.
On the particular of abortion, in terms of liberty, the baby's liberty must be considered, not only the mother's.
In the general case of state vs federal sovereignty, state sovereignty is closer to the individual is and more malleable/escapable than a federal sovereign, and is thus preferable (state sovereignty was the original ideal of the United States and the founders go on at length about the benefits of this arrangement.)