Why doesn't the man kill himself and the child in order to escape the fallen world?

The man simply can't do it. The easiest thing in the world for him to have done after his wife's suicide would have been to join her in death, but he can't. Maybe it was fear, and maybe he just couldn't bring himself to take the coward's way out because he had a young son with a life to live. Regardless, they take off together in a bid to survive.