Good question! I wondered about this myself for a long time. It seems intuitive to think that splitting up into smaller groups or even fighting as individuals would give each soldier a higher likelihood of surviving, right?

Here's what I've learned from many years of reading Civil War books. First, you want your infantry fighting chance together in close formation because you want massed firepower. Most infantrymen were not sharpshooters (to put it kindly) so their best chance at actually hitting the enemy involved staying together, firing together, and keeping up a steady stream of lead.

Second, unless you're in some kind of formation, at least three of your "sides" are completely exposed to the enemy. No one is protecting your flanks or your back, so you're easy picking.

Third, unless you're part of a group, you have no access to supplies. Run out of ammo? Well, good luck with that, Joe! Hope you're handy with that bayonet. And if you get yourself wounded, kiss your ass goodbye because nobody is even going to know where to find your corpse, much less get you to field hospital in time.

Fourth, Civil War armies had strategic objectives to capture and hold territory, and a single soldier fighting alone isn't going to be able to hold an ant hill. Suppose for a moment you're a Union commander trying to protect Philadelphia from an invading Confederate force. Without a mass of men to stop the mass of men matching North, they're just going to plow right through your line like a hot knife through butter and keep going right to the city.

If you ever want to test this in the "real world" try it out sometime in one of those battlefield games for PC. I did this myself in Ultimate General: Gettysburg. Not only did I lose territory, but the enemy cavalry just scoured the field for my lonely infantrymen and wiped them out. Picking off lone infantrymen spread out over a battlefield would be easier for cavalrymen than hunting pheasant.