I have wondered about this myself: why did the Confederates not put the right to secede explicitly into their Constitution? Were they hypocrites who wanted the right to leave the US themselves, but did not wish further secession once they were in power? Or did they simply believe that such a right was understood and did not need to be spelled out? Marshall DeRosa has the answer:
The Question naturally comes to mind, if the CSA was committed to a states’ rights doctrine, especially in light of the historical developments of the antebellum period, why did the states not expressly constitutionally mandate a state’s right of secession? The answer to this question is threefold.
First, the framers of the CSA Constitution contended that they were seceding on behalf of the US Constitution, and not because they were opposed to its principles…Their affinity for the US Constitution included the understanding that it did not deny the right of secession but implicitly protected that right as a prerogative of state sovereignty. They claimed it was fallacious construction that had cast doubts on the right of secession. To draft their Confederate Constitution with the expressed right of secession would, it was claimed, be yielding to the Northern interpretation of the US Constitution that if such a right is not expressly granted, it does not constitutionally exist. This they were not about to do.
Second, the seven Southern states that had initially seceded from the Union had the practical problem of attracting the variable border states into the Confederacy. Virginia was especially reluctant to join a confederacy lacking a viable central government. To mandate constitutionally the right of secession would give the appearance of a loose league of disparate states held together by a feeble central government, not destined to endure…Consequently, the CSA framers decided to make the right of secession constitutionally implicit by explicitly recognizing the “sovereign and independent character of the States,” thereby providing the central government with the appearance of viability that otherwise might be lacking.
And third, and most importantly, the CSA Constitution has a covenant component, establishing a central government held together by the consent of good faith of its members, not by coercion. In other words, it is a voluntary association grounded in a transcendental order. In this context, “a covenant differs from a compact in that its moral dimensions take precedence over its legal dimensions. In its heart of hearts, a covenant is an agreement in which a higher moral force, traditionally God, is either a direct party to or guarantor of a particular relationship. Whereas, when the term compact is used, moral force is only indirectly involved.” "The Confederate Constitution of 1861: An Inquiry Into American Constitutionalism" - Marshall L. DeRosa