When in the course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain inalienable rights, that among these are life, liberty and the pursuit of happiness.
That to secure these rights, governments are instituted among men, deriving their just powers from the consent of the governed. That whenever any form of government becomes destructive of these ends, it is the right of the people to alter or abolish it, and to institute new government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their safety and happiness.
I have highlighted important words and phrases for your comprehension.
The Confederates were doing exactly what the Preamble to our Founding Principle says we are REQUIRED to do! Not that we have the option of doing, not that we have the legal justification to do, but what we are REQUIRED to do, if we hold the truths to be self evident and believe in our founding principles.
The reason people have a difficult time comprehending this profound point, is because in 2010, we just can't wrap our minds around the prevailing "intellect" of the day! We tend to presume that people could look at a black person and see a person who is black, because that is what we see today, we can't imagine how anyone could have seen something different in 1860. It doesn't seem like that long ago, really... 150 years? In the scope of humankind, that isn't too very long ago. So it doesn't 'compute' in our brains, just how far we have come.
In 1860, a black person was not seen as a person. They were called "Negros" and the prevailing intellectuals of the day, argued they were not of the human species, they were not "people" but more like "missing links" in the evolutionary chain... much of this is thanks to a young scientist named, Charlie Darwin. White people, by and large, viewed them as "black savages" and not people, certainly not as advanced as white society. So, the liberties and freedoms spoken of in the Constitution, simply did not apply to these "creatures" from African jungles, any more than it would apply to Gorilla's in a zoo!
Now, certain liberals here will have us believe this view was only among people of the South, and the more sophisticated Northerners were akin to the liberal elites of today, and didn't have any prejudice toward black people whatsoever! This is simply a false perspective, and ignorance of the way people thought in 1860. During that time, slaves were thought of as property, because the courts said they were property, not people... property! With the exception of a few Mormon's and Quakers, most white people didn't even consider them humans.
When you take into context this prevailing thought and the law of the day, the Southerner's did have a legitimate complaint with regard to what the Constitution says. If that was "wrong" the Constitution should have been changed, or the courts should have ruled differently regarding slaves being property, but that wasn't the case. There had been plenty of opportunity for someone to have changed things, but they didn't. So when things came to a head, the Confederacy did precisely what our founding documents compelled them to do. It wasn't unconstitutional, it was their obligation.