Lincoln’s immediate goal ca. 1861 was not to abolish slavery. The average early Union volunteers main motivation certainly wasn’t.
However, the secessionists’ main reason for seceding was a belief that Lincoln’s election meant eventual abolition. See the South Carolina secession declaration. Slavery is pretty much all it talks about, the North’s long history of lack of good faith (eg wrt Fugitive Slave Law enforcement) and the last straw: “the election of a man to the high office of President of the United States, whose opinions and purposes are hostile to slavery.”
http://avalon.law.yale.edu/19th_century/csa_scarsec.asp
And eventually during the war and after a more openly abolitionist faction of the GOP came to the fore. Anger toward the secessionists over the war’s terrible cost was a catalyst, but not that long after the election of Lincoln slavery was in fact abolished: the secessionists’ fear turned out reasonable, though exacerbated by their own actions.
The excessive downplaying in the US nowadays of slavery and abolition as factors in the Civil War is driven from two sides:
- Southerners (not necessarily all conservatives or just truly conservative Southerners) who want to honor ‘their heritage’ in the CSA and particularly its military without dealing with the moral stain of slavery that cause fought to preserve.
- Left leaning people everywhere who go to any length to avoid looking like Stewie in Family Guy where he gives an unsolicited ‘you’re welcome’ to a black guy when touring Gettysburg. That attitude is obnoxious indeed, but the Union sacrifice was in fact in part, and increasingly as things developed and the cost rose, about freeing the slaves. Though not about racial equality, which isn’t the same thing.