Wikipedia’s actually pretty good for this…

Quick summary would be that the 10th Amendment says that any power not given to the federal government is reserved to the states, so the slave states argued that the feds shouldn’t interfere in their slaving.

Then when Lincoln was elected President the Confederate states seceded, bringing the Preamble to the Constitution into relevance; in his inaugural address Lincoln argued that the phrase “to form a more perfect union” implied that secession was illegal – that the federal government had been established as having power over the people directly rather than being an agreement between the states as the Articles of Confederacy had been.

The Confederacy wrote their own constitution, but it was mostly verbatim from the US constitution. They added some protection for slavery and added some rights for the states, took some other rights for the federal (confederal?) government. Full explanation here.

That help?