The 3/5 compromise allowed the Southern states to count 3/5 of their slaves towards a states population, therefore giving them more representation in the House of Representatives. Of course, the South wanted to count them all (while denying them citizenship, and merely referring to them as property), while the North didn't want the slaves in the population count period. The compromise was necessary or we might not have the Constitution as we know it today. Slavery itself was racist, thus, from it we have racist policies.
As far as the secession of the Southern states goes, the issue wasn't about representation in the House of Representatives at all. At the beginning of the Civil War, there were about 22 million people in the North and about 9 million people in the South. Of the 9 million in the South, about 4 million were slaves. Count 100% of those slaves, and you still have an overwhelming majority of northern representation in the House. The issue was the balance of power in the Senate. The South was outvoted in the Senate on every bill concerning slavery or states' rights, and when Lincoln was elected, the South felt that the country had elected an abolitionist, and that they no longer had a voice in the national government. By the way, Lincoln was not considered, nor did he consider himself, to be an abolitionist. He said slavery was wrong, but he simply wanted to keep slavery from spreading to the western states. Remember, the definition of an abolitionist was someone who wanted to abolish, or end slavery.
Oh, and by the way, it is the Declaration of Independence that states "all men are created equal", not the Constitution.
