Well it's good that you regard Abe Lincoln as a valid authority regarding why the war was being fought, because he makes it very clear in his letter to Horace Greely.
My paramount object in this struggle is to save the Union, and is not either to save or to destroy slavery. If I could save the Union without freeing any slave I would do it, and if I could save it by freeing all the slaves I would do it; and if I could save it by freeing some and leaving others alone I would also do that. What I do about slavery, and the colored race, I do because I believe it helps to save the Union; and what I forbear, I forbear because I do not believe it would help to save the Union.
I take his word at a little over a year into the war more than I do his efforts to justify what he had already done by three years later.
Having wrecked the South, and having wrecked slavery, what is he going to say? That he fought the war to force the South back into the Union? Why was that worth the deaths of 600,000 people? No, the necessary political optics required something more noble than forcing subjugation on a group of people who didn't want it.
The rationalization seized upon was "abolition of slavery", not because it was true prior to the fact, but because it was something he believed the public would accept. People were deeply religious in those days, and would believe that it was "God's Will" to fight in a noble cause.
Clever Lawyer/Politician, He. Too clever by half.
Not to mention, I have yet to look up the letter from Greeley that Abe was responding to.