Henry has very romantic ideas about war when he first gets started. The reality of war does not hit him until later in the book. Then he begins to get depressed. He sees the carnage on the battlefield, and decides it's better to be dead than injured.
Henry was worried about many things, including how he would react under attack and whether he would "skedaddle" under fire. He also questioned the leadership capabilities of his officers and whether his comrades were worthy of being trusted with his life. Death would solve these problems, and he believed it would be a welcome "rest."
Once he thought he had concluded that it would be better to get killed directly and end his troubles. Regarding death thus out of the corner of his eye, he conceived it to be nothing but rest... He would die; he would go to some place where he would be understood. It was useless to expect appreciation of his profound and fine sense from such men as the lieutenant. He must look to the grave for comprehension. (Chapter 3)