The CSA was certainly not half of the United States at that time. They inflated their numbers with the "3/5 compromise". Even with that method of inflating their representation, 11 states with 66 House Representatives seceded, while 23 states with 173 House Representatives did not secede. It wasn't close to half.

On top of which, the decision process for secession was (shockingly, I know!) not democratic in the least. The Union didn't need a "Home Guard" to enforce conscription, but the South did.