There is only one answer included here, and even that is incomplete. What are our choices?
The sentence is drawing a parallel between the two parties' reasons for going to war. Each of them is associated with a verb: one with "survive," the other with "perish." They are the two antonyms.
Antonyms are words which have opposite meanings. <em>Survive </em>means to contine living, and <em>perish </em>means to stop living.
What Lincoln meant by using this antonym-based parallelism is that the Confederacy fought to end the exisiting nation (meaning, to secede from the North and create a new nation), while the Union fought to keep the nation alive by preventing it from splitting.
