Even assuming that is true, it makes no sense as a reason to secede. Assuming the Civil War never happened, they would still have lost all political influence by seceding.
The whole conflict was about territories. It is not like north would care what happens to slaves in the south.
There was balance - half states slave states, half not. Territories being not slave states would disturb balance. They feared being outvoted. They feared that territories being not slave states would be addmission that slavery is wrong and put pressure on them to stop slavery.
Seceding makes you completely independent. You dont loose power, you gain it.
