The 3/5ths compromise is so misunderstood. Southern, slave-holding states wanted the slaves to be counted as people for the purpose of apportionment for of Representatives and Electors for President. Northern, non-slave states said they shouldn't be counted since they weren't going to be citizens. By counting them as 3/5ths of a person for the purposes of apportionment, it bolstered the power of the Southern states (who had a much smaller White population relative to Northern States) in the legislature and allowed them to come to terms and agree to move forward with the Constitutional Convention. It's convenient how people who misinterpret the 3/5ths compromise also generally neglect the "and Indians not taxed" portion of the clause, which is meant to draw distinction between those paying taxes and submitting to the power of the State and those who weren't.
For the tl;dr crowd, the South wanted to count them as 5/5ths of a person and the North wanted to count them as 0/5ths of a person.