If slaves were counted in the South's population, then the South would have a lot more people in their population than the North. This would affect the House of Representatives, where the amount of representatives each state has is determined by population (larger states have more representatives).
If that were to happen, the South would be able to vote on laws and get laws passed that followed their beliefs. The North wanted to make sure, as they, at the time, had a larger population of non-slaves, that they would stay in control of the House of Representatives.
Eventually, the nation agreed on the 3/5th Compromise, where slaves would count as 3/5th of a non-slave person.
