Most people don't have any understanding or appreciation of the idea of states rights because 1.) more liberal politicians (who are generally imitating European politcal theory) are always trying to convince us that more government is better, by which they mean of course more national government. Marxism, Socialism - these political theories have almost nothing in common with Federalism (one of the primary political systems our country was founded upon) on any level; 2.) it is just a reality of modern technology and communication that as a nation we feel more unified than ever in terms of geography and less like loosely joined states. In 1900 a trip fom South Carolina to Austin, Texas would have taken probably 2-3 weeks. In 1850 it would have taken 4-5 weeks. In 1800 it would have been impossible. Now it takes 2-3 days by car, 5-6 hours by plane. That is simply astonishing, and it is no wonder we think of ourselves more as a collective unit than of an amalgamation of individual entities; 3.) our education system is getting worse and worse and few people seem to know much about our national history at all, that is short of what they learn in blockbuster movies of course!

Most people probably know that today the details of taxation and certain other matters, such as drivers licenses and legal documents differ from state to state, but they do not put 2 and 2 together and realize that our country was originally a compromise between a pure federalism where there was practically no centralized government and a (then) British style government with a single ruler or rulers and some sort of legislative assembly/assemblies. The compromise involved certain rights, such as national security, foreign policy, etc. to be placed in the hands of the central national government while issues like taxation, education, etc. were left in the hands of the state govrnment.
This is the context behind which the Civil War took place. (Southern) States felt that there were specific domains into which the national government had no right to interfere. This seems strange to modern Americains for the reasons I listed at the beginning, but in reality this compromise between cetralized and decentralized governmental units was a fundamental tenant upon which our country was founded, as fundamental as the Constitution itself inasmuch as it was the tenant upon which many sipulations in the constitution itself were founded. When you understand this, the southern states balking at the interference of the central government into matters that had traditionally been the domain and right of states to handle does not seem so strange or extraordinary. Sure slavery was a big issue, but it was a catalyst and as I hope I have demonstrated there were serious ideological issues of government behind the Civil War - it wasn't, as is often supposed, just a bunch of racist southerners who prefered to die rather than give up their slaves.