The body politic in the Southern States was not premised upon some "one man/one vote" assumption, such as led to genocide in Rwanda. As in ancient Athens, "Democracy" was premised upon a recognized citizenry. Athens had both a large foreign resident population & a large slave population, at the time it defined the "Democracy," which some people--not the Founding Fathers--but some people, considered an ideal.
Naturally, it was the recognized citizenry, whose liberty was being pursued. On the other hand, many Confederates would have argued that their secession would also have protected the Safety & Happiness, of those held in service. You can garner a feeling for this, should you elect sometime to read some of the literature of the period.
I fully understand the context, and also fully understand that there were many people at the time of the Civil War (and even, to a much lesser extent, at the time of the Declaration) understood that the Declaration does not say that all Citizens have inalienable rights, but rather that all Men have inalienable enable rights, and therefore that chattel slavery was fundamentally incompatible with the ideals set forth in the Declaration. This is not a revisionist concept.