Listen real close, Lincoln refused to parley with at least two peace delegations. One from Jeff Davis appointed representatives and one form Virginia. That is classic Lincoln he says one thing and does another, he was the slimiest President to ever darken the white house.
This is true, and it does show that Lincoln was less than competent in his initial handling of a situation that could have been defused politically, thereby preventing war (and coaxing southern states back into the Union). It doesn't follow from this point that secession at will is Constitutionally authorized.
Lincoln's response to your view, from his second inaugural:
"On the occasion corresponding to this four years ago all thoughts were anxiously directed to an impending civil war. All dreaded it, all sought to avert it. While the inaugural address was being delivered from this place, devoted altogether to saving the Union without war, insurgent agents were in the city seeking to destroy it without warseeking to dissolve the Union and divide effects by negotiation. Both parties deprecated war, but one of them would make war rather than let the nation survive, and the other would accept war rather than let it perish, and the war came."
-- Abraham Lincoln, second inaugural speech