The main reason is that if you were to try to use modern infantry tactics on a 19th century battlefield then you would likely be run down and slaughtered by cavalry. Obviously that sentence is a very facile summary, but it gets the gist of it. The primary factor is density of fire, the more 'firepower' you can put out, the more dispersed you can and should have your troops. Remember that in the American Civil War people were primarily using muzzle loaded rifles and this imposes several considerations:

1. They are quicker to reload when you are standing up.
2. They do not fire terribly quickly, four times a minute at best with three common.

Now according to 'Regulations for the Instructions, Formations, and Movements of the Cavalry', which was issued in 1851 for the British Army, cavalry at the gallop should move at eleven miles an hour. This means that in the time it takes to reload and fire a minie' ball rifle, cavalry will likely have moved around a hundred yards closer.

An infantryman simply does not get many opportunities to shoot if cavalry are moving to charge them, dispersed riflemen are not going to be able to hit enough charging cavalry to avoid being massacred when they close.

Of course during the course of the war people did realize that they had enough firepower to employ more flexible formations than were used in the Napoleonic Era and this did alter tactics, but they were not stupid to resist spreading out and trying to fight like modern infantry, if you got the estimation wrong then there was that very real risk of being ridden down and killed.

Here is a good source on the evolution:

http://www.dtic.mil/dtic/tr/fulltext/u2/a227467.pdf

Keep in mind that even generations later with bolt action rifles, cavalry were still a deadly threat to unformed infantry. In the early stages of combat on the western front in World War 1 cavalry were still very effective, at for example the Battle of Mons.