In the South those individuals were considered property and not people. They had no rights and therefore no need for congressional representation. As a result the white population was over-represented in the House.
Slaves were not considered merely property, not people, in the South, though things were headed in that direction when the war broke out.
After all, as I believe Lincoln pointed out, nobody makes laws punishing cows or dogs for misbehavior.
The only logical way to maintain a claimed belief in the principles of the Declaration of Independence and in the positive rightness of slavery, of course, is to decide that slaves, or possibly all blacks, aren’t really human. Which is the tack the Dred Scott decision pointed to.
Once one starts down this road there is no logical stopping point. If people of African ancestry can be considered sub-human, why not of Asian or Italian or Jewish ancestry?
Or one can simply decide that Jefferson et al were in error, and that all men are NOT created equal. This is the approach Calhoun, Stephens and other chose.