Answer:
(1) He knew that that Emancipation Proclamation was on shaky legal grounds once the war was over. (2) He knew the great strength of the Slave Power and its allies in the North; he didn’t know if promises of emancipation would be honored by governments that came after he left office unless slavery was abolished by the Constitution. (3) While he had appointed Republican judges to the Supreme Court, including the abolitionist Salmon P. Chase as the Chief Justice, he knew that courts can come up with unexpected decisions (for example a determination that the Emancipation Proclamation applied only to those who had crossed Union lines during the war or that it didn’t apply to children of the former slaves); (4) the nation needed to get beyond the issue of slavery before it could progress or as the Lincoln character in the movie said,
. . . I can’t accomplish a thing of any human meaning or worth until we cure ourselves of slavery and end this pestilential war, and whether any of you or anyone else knows it, I know I need this! This amendment is that cure! We’re stepped out upon the world’s stage now, now, with the fate of human dignity in our hands! Blood’s been spilt to afford us this moment!