The Declaration formalized and stated the reasons for the Revolution against British rule, which in fact had been in progress for more than a year. It was not an act of secession, but was an act of rebellion. No one at the time even contemplated that they had a right to secede under British law. But they did claim the right to Rebel under Natural Law and the Declaration laid out their moral justification for that rebellion.
In 1861, the Confederacy laid out no such moral case for their rebellion for one simple reason --- they had no moral case to make. That is why they invented a flawed and entirely fictions legal justification called a right to secede at will. The Constitution never granted such a right, and even prominent Southerners knew it didn’t.
"Secession is nothing but revolution. The framers of our constitution never exhausted so much labor, wisdom, and forbearance in its formation, and surrounded it with so many guards and securities, if it was intended to be broken by every member of the Confederacy at will. It was intended for "perpetual union" so expressed in the preamble, and for the establishment of a government, not a compact, which can only be dissolved by revolution, or the consent of all the people in convention assembled. It is idle to talk of secession. Anarchy would have been established, and not a government, by Washington, Hamilton, Jefferson, Madison, and the other patriots of the Revolution."Robert E. Lee Jan. 23, 1861