Did the Southern slaves have the right to reform a society based on slavery? I don't think the Confederate "champions of liberty" thought so. The same secessionist leaders who whined about the "oppression" of the Union had no moral problem with treating a whole race of people as potential property. This moral contradiction is just one of the reasons that the rebellion was illegitimate and doomed to failure.
Of course they had the right, plainly explained in the Constitution. Which is why it is important we defend it today because there are many who would like to see slavery return in a updated form i.e. socialism.