Why did Henry feel pity toward Wilson's shame?

This is because Henry understands the brutality of war. He understands how it almost instantly turns boys into men. There is no arrogance in battle.

Henry feels pity toward Wilson's shame because he is now confident that he does not have to feel the same. See the following:

His friend at his side seemed suffering great shame. As he contemplated him, the youth felt his heart grow more strong and stout. He had never been compelled to blush in such manner for his acts; he was an individual of extraordinary virtues.

He reflected, with condescending pity: "Too bad! Too bad! The poor devil, it makes him feel tough!"