it depends on what you mean by "rights" (ooops do I sound like Clinton? LOL

Might it be said that the South seceded because she was fearful of losing the RIGHT to own slaves; had already lost the RIGHT to a proportionate share of Federal revenue; had (apparently at the time) lost the RIGHT to secede and, upon Lincoln announcing in April 1861 his intention to raise 75,000 Yankee troops had become fearful of losing the RIGHTS afforded by First, Second, Third, Fourth, Fifth, Sixth, Seventh, Eighth, Ninth and Tenth Amendments, otherwise known as the Bill of RIGHTS.

Seems to me that when secession was complete, the loss of or fear of losing RIGHTS had much more to do with secession than mere slavery alone.