They wanted a strong Federal government when it suited them, and a weak Federal government when it suited them. It wasn’t a matter of a general principle - it came down to economic interests, and the economic interests of the South were built almost exclusively around slavery. The Confederacy was more centralized in some ways - such as the absolute prohibition against states’ rights to regulate slavery - but in others, it was weak, such as the right of individual states to nullify Federal (or, rather, Confederal?) officers in their state.