Which parts of this excerpt from Jefferson Davis's Inaugural Address suggest that the Confederate States' decision to secede from the Union was motivated by their desire for freedom?

I don't know what specific excerpt you have in front of you (since you didn't share that), but twice in his inaugural address Jefferson Davis spoke of the Confederate States acting for the sake of liberty. They saw their cause as one that preserved their freedom or liberty as states.

Here's one of those sections from his speech:

The declared purpose of the compact of Union from which we have withdrawn was "to establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessing of liberty to ourselves and our posterity; " and when, in the judgment of the sovereign States now composing this Confederacy, it had been altered from the purposes for which it was ordained, and had ceased to answer the ends for which it was established, a peaceful appeal to the ballot-box declared that so far as they were concerned, the government created by that compact should cease to exist.

Here's the other section, right at the end of his inaugural address:

It is joyous, in the midst of perilous times, to look around upon a people united in heart, where one purpose of high resolve animates and actuates the whole--where the sacrifices to be made are not weighed in the balance against honor and right and liberty and equality.