I think there was a story arc sometime in the late '90s or early '00s where he tried to be Superman at all times. I haven’t read it myself and don’t know how it was resolved, but that might be a good place to look.
Strategy is a little harder since the objection is so vague in the first place. I suggest What’s So Funny About Truth, Justice, and the American Way? That could cover it.
And as a general jumping-on point for a reader skeptical about Superman, John Byrne’s Man of Steel miniseries might be a good place to look.
Overall, though, I find Superman haters to be aggressively unreasonable on the subject. These aren’t the objections you usually* hear, though, so there might be some hope for your friend.
*Things like “he’s overpowered” or “he’s boring” that aren’t remotely defensible if you actually read any half-decent Superman comics, but are used by people as an excuse not to.