Point is: nobody fights for "stalemate".
Especially early-on Confederates hoped to win enough battles to call any peace settlement a decisive victory.
That's simply indisputable.
With a small industrial base, a pretty good Union Naval blockade choking the CSA and out numbered 3:1 do you really think the people of the South are that dumb to think that they could invade/conquer/occupy the North?
I think what is going on is that history is written by the victors and they want to portray the North in this existential perilous fight against a Southern invasion which is preposterous, funny and exactly the opposite of what actually happened.