Why didn't president Lincoln allow South to separate in peace?

Some think that Much of the revenue (what we would today call "gross domestic product") of the United States at the time came from the export of agricultural goods produced in the Confederate states. Political and philosophical concerns aside, the Union simply could not afford to let its most economically productive states go.

Not entirely true-the north was producing textiles and steel along with most of the "real goods" that were made from raw material in the states. they managed to bankrupt and beat the south because even though the south had the manpower they did not have the mills, foodstuffs, raw materials including even ammo for their guns much less the guns themselves. Southern soldiers were very literally starving and without shoes long before the war was over. And so were a good part of the people, so that when sherman burned and pillaged in his march to the sea it was the breaking point because they had nothing after that to fight with. Southern strategists gambled and lost because they thought they would break the north with early victories. Yes the south had some economic clout but they were terrified that they would have to compete with everyone on a level playing field as far as their agricultural economy fueled by slave power being subverted and being made to actually pay hired help. They lost all the way around because Britain started to grow cotton in Egypt and realised they didnt need the south.