In short, because it served no real military objective. Starting in 1863, the Union certainly began to shift its posture to a footing that allowed for the destruction of Confederate resources as a means to attack their enemy's ability to prosecute the war, but this never included a large-scale effort to target civilians themselves. It was considered enough to go after food stores, livestock, agricultural concerns, and other industrial centers (or railroads) to cut into the Confederacy's logistic underbelly. Committing resources to target civilians simply wouldn't have served a justifiable purpose.

Now, there were instances where civilians got caught in the cross-fire of battle, or were tangled in the practical realities of a campaign (like in Vicksburg, where many city residents refused to evacuate despite the shelling of the city). But early on, the Lincoln administration made it clear that they didn't want to unduly punish Confederate citizens during the course of the war, as there was always a thought about how the country would reconcile after hostilities ended. This is why the more aggressive actions of Grant and Sherman (and later the rest of the Union Army) only came about after roughly two years of fighting. Things were grinding forward slowly, and Grant realized that an army could live off the conquered territories on a march whilst simultaneously depriving the enemy of supplies. This double-bonus realization didn't necessitate a direct attack on civilians, which would have been a major escalation in the nature of hostilities that industrialized, large-scale warfare wouldn't really see for another 80 years or so (which is not to say that it was new to the 20th century, just latent, or dormant, if you will).

Lastly, there really was a chivalric component to the who affair, with both sides influenced by idealistic, dramatic notions of gentlemanly behavior. This wasn't the only consideration, and its effect shouldn't be over-stated since it didn't really extend beyond attitudes towards white people (and also because the American Civil War was effectively a large scale butcher shop), but it did play into how attitudes on both sides developed and evolved.

[Sources - Jay Winik, 'April, 1865'; Bruce Catton, 'Grant Moves South' & 'Glory Road'; James McPherson, 'Battle Cry of Freedom']