Your statement makes no sense. Think of the classical personal rights metaphor, “Your right to swing your fist ends at the tip of my nose.” In more abstract terms, your rights should be uninpinged until such point that they impinge on my rights, premised by the agreement that our rights are equal otherwise.

Now let’s look at state’s rights. If state’s are required to allow slavery, that is giving more rights to the states that have slavery than it is to the states that don’t. If slavery are required to not allow slavery, that is giving more rights to the states that don’t have slavery. The stance that best reflects state’s rights as being equal unless they impinge on the other states is to allow those who want slavery to have it and to allow those states that don’t want slavery to abolish it. From a practical standpoint, that also means that bringing your slaves to a state that abolishes slavery frees them, otherwise the laws from your state have greater authority than the laws of the state you are actually operating in, which doesn’t meet the basis of equal unless they impinge. That also means if your slaves escape to a free state, it is your responsibility and not the free state’s to stop them from entering that state, and certainly returning them isn’t an obligation since that would violate their law that no person can be enslaved.

As has been pointed out previously, this was the state of things until a federal law was enacted to reduce the rights of the states who opposed slavery, which wasn’t enforced adequately (in the opinion of the slave-holding states).

So, if you want to use the fig leaf of the Civil War being about state’s rights, then the only way that makes sense is if the seceeding states wanted states to have fewer rights, not more. Of course, there is also the option of denying reality and saying whatever makes you feel best, facts and logic be damned.