Actually they did. They could have not started the war, but instead chose to do the opposite. They could have prevented the Union army from campaigning in Confederate territory, but had neither the numbers or the leaders to do that. They could have taken the war into the North, but their attempts at that proved to be ineffective if not downright disastrous. It is not their choice to keep the war going, it was the Union reasons that kept the war going. They had a lot of choices but when they blew it on the first one, not starting the war to begin with, then the others were bound to fail as well.
Once again I point out to you, that if "slavery" was the reason and the only reason why the confederates fought, then why didn't they simply rejoin the Union? Lincoln was saying they could keep their slavery, and they had it before Lincoln became President, so why would they fight for something which the other side was willing to give them?
Because having left the Union before Lincoln was inaugurated and having adopted a constitution with protection for slavery far greater that was ever possible under the U.S. Constitution, even had the Corwin Amendment been ratified, what reason would they have had to end secession and return?
The facts simply do not support the contention that either side was fighting over slavery, because slavery was not being threatened by the war. (at first.)
The facts do, as do the writings and speeches of the Southern leaders of the time. But you do not accept that, preferring to believe that it was all Lincoln's fault. So be it. It means that there really is no point in continuing this useless discussion.
Judging by Pea Ridge's posts concerning the messages and letters regarding the ships sent to Ft. Sumter, it does not look like they had that choice either. The evidence indicates Lincoln was going to have his war one way or the other.