As the parent points out, what's potentially wrong with this method is the absence of cost benefit-analysis based on what value this will provide vs. any negative effects this will have (in addition to the actual cost).
Your argument is an instance of "we should do something; this is something; therefor we should do it."
On the other hand, the parent's argument is the classic "Some random edge case might happen, therefore it's not worth doing X" argument. You're right, the absence of an actual cost-benefit analysis makes this debate somewhat pointless.
Why is it wrong to look at the issue from a cost/benefit perspective? If an expenditure of resources isn't very effective at preventing child abuse, shouldn't those resources be deployed in a different way so we can prevent as much abuse as possible?
Benefits include things like "fewer children getting abused".
Costs include things like "children in formative years being told that a beat up child looks perfectly normal". (And, as hawkw mentioned, "opportunity cost of not being able to implement other strategies".)
"Think of the children!" is a potentially dangerous slippery slope argument that, on Hacker News, we often deride because of where it can go, where no logic and only emotions are thrown into the mix.
It just so happens that, in this case, you're actually affected by the argument being presented. Child abuse is an absolutely terrible thing, and we should work to stop it, and work to get those children that are being abused a way to be protected, and so on; but the question that others here are asking is "is this the right way to do it? Will this attempt do more harm than good?" and that's a good question to ask.
If 5 year olds everywhere are taught that black eyes are not potential signs for abuse, then Billy down the street might get missed, because mom didn't see the what the child said, when the kid, seeing the billboard, asked why "why is that kid hurt?"
