It basically means there's no way that it could not affect him.

It means "It could not avoid affecting him." "It could not do anything else but affect him. "It had to affect him." "It affected him; it was impossible that it could not." "Could not but" is a colocation. It's a little literary and old-fashioned. I can't really explain why it means what it means! Here are some examples of use. "I didn't know the best way to learn Spanish, but I was sure that setting my computer to use Spanish could not but help." "The poor unhappy gentleman’s grief came into my head again, and indeed I could not but shed tears in the reflection upon it." (Daniel Defoe, 1772) It was so sad that he couldn't resist crying. "it was a degree of wilful thoughtlessness which Catherine could not but resent."--Jane Austen, "Northanger Abbey," 1812. It was too thoughtless. It was so thoughtless she couldn't possibly forgive it. She had to feel resentful.