Why do you believe the south wanted to maintain an equal balance between slave states and free states in the Senate?

If you have more slave states then free states, or more free states then slave states, voting wouldn’t have been equal and fair. More of one side will result in an unfair voting, because free state citizens would want to vote for a president who is against anti-slavery, like Abraham Lincoln, and slave owners living in slave states would want to vote for a president who is pro-slavery. Having an equal number of free an slave states makes the voting equal, and makes everyone have an equal representation in congress.

Hope this helps :)