Forces lose battles because of a combination (1) they didn't have enough committed, undamaged survivors (for victory calculation), and (2) they didn't damage enough of the enemy (to make them unavailable for victory determination).
The former is addressed by the leadership/commitment rules and victory determination rules. The reason the CSA is typically so successful throughout the game is that in the battles they chose to fight they have sufficient quality leadership (infantry rating 3 or 4 of corps and army commanders) that all or almost all of their troops fight !! The USA can achieve this too, but typically not until fall '62 and later. Let's face it, the USA is swimming in infantry capability 2 generals.
Not doing enough damage is the other problem. Obviously of first important is getting one's troop committed (per above). This is why Lil Mac at 2-2-3 is generally better to have than Halleck at 2-3-2 or McDowell at 2-2-2. Remember, they can't shoot if they're not in the battle.
Once the troops are committed, the important thing is how effectively they shoot!! Read the modifiers in the rule book. With CSC, each unit has a division commander, a corps commander and possibly and AC adding to both the commitment and attack/defense ratings.
An important assessment tool available to both players through the replay button is the individual die rolls of the firing (attacking/defending) unit. When your die roll is consistently modified to -6, you should figure out why. You'll seldom get hits with
a -6 modifier, so you need to notice, identify and fix the problem.
This game system is not so much unfathomable as complex.
Have fun !!
"L'audace, l'audace, toujours l'audace."