They didn't; There were many nuances to political opinions about slavery and the abolitionist movement (which was far from monolithic itself) understood that. Lincoln was not an abolitionist, but he was not proslavery either. He was what was known as a 'freesoiler.' Lincoln believed that slavery's expansion should not be allowed in new states. This was not an uncommon belief among white westerners like Lincoln; the logic was that the presence of slavery devalued free labor and made things much worse for poor and middling whites.

For radical abolitionists, the fact that Lincoln believed in colonization (the forcible deportation of free Blacks to Liberia) particularly rankled them, as the abolitionist movement had been vociferously anti-colonization since the 1830's.

Sources: All on Fire by Henry Mayer and Samuel Joseph May and the Dilemmas of the Liberal Persuasion 1797-1871 by Donald Yacovone