You might think that on the battlefield, everyone's an equal. After all, everyone's equally likely to kick the bucket, right? Well, maybe not. After all, the speaker of "The Man He Killed" is an enlisted infantryman, which means that on the battlefield, he was on the front lines, taking orders from someone way in the back. And in all likelihood, the fact that he was an enlisted infantryman probably stems from the fact that he wasn't the richest of dudes on the home front. So it turns out that, like everything else in life, the battlefield isn't always an even playing field.
The real lesson of this poem is not that war is Hell, but that war is Hell for the lower classes.
The fact that this guy may have joined up because he was unemployed tells us that it's the lower classes that suffer most in war.