A city Health Department official committed a major political gaffe last month: She spoke honestly about problems with school feeding programs.

Community Epidemiology Director Gretchen Van Wye revealed that the school-breakfast program results in nearly a quarter of kids getting two breakfasts a day. More, she suggested that this overeating might contribute to higher obesity rates among poor children, and that schools try to ensure children aren’t inadvertently taking in excess calories by doubling up on the meal.

For this, Van Wye has been called “horrible”; one school official even told The Post he “shudders to think it’s even being discussed by researchers.”

I’m sure the idea is troubling to some. Heaven forbid that facts reveal these programs to share some blame for poor kids’ obesity. But those truly concerned about children’s welfare should take the revelation seriously.

Her discovery reveals an important piece of information: Some kids are still being fed at home by their parents even though their parents qualify for food-assistance programs.

The idea behind these programs is that we really can’t expect poor parents to feed their kids.

That logic goes something like this: Poor parents work multiple jobs and don’t have time to pack their kids a lunch, so the government should step in. Poor parents can’t be bothered to feed kids breakfast, so government needs to add breakfast. The federal Agriculture Department has even expanded the schooldinner program to all 50 states out of a supposed concern that parents can’t manage to put together a simple dinner for their kids.

This patronizing characterization of poor parents helps make the case for greater funding for feeding programs. But those efforts carry a number of unintended consequences.

For starters, as kids eat more and more institutional food prepared at school (not in their own kitchens by mom and dad), kids might get a sense that their parents really don’t care about their nutrition decisions. Parents may also start to assume their children’s nutrition is someone else’s responsibility.

That’s bad news, since studies show parental involvement is critical to a child’s healthy development. In fact, First Lady Michelle Obama herself promotes the idea of greater parental involvement in children’s nutrition.

Van Wye’s critics caricature her as indifferent to children’s suffering, wanting to snatch bran muffins out of the bony hands of starving children, but her actual recommendation shows that she simply believes that school-meal programs need oversight and that parental involvement would be a healthy additive.

The Agriculture Department isn’t listening; since Van Wye made the news, it has announced new rules to make school meals more “healthy.” Beyond adding more whole grains, fruits and vegetables, the guidelines also call for increased funding and automatic enrollment for poor children.

Bottom line: The only “acceptable” rethinking of school meals pushes for more funding and higher enrollment. A solution that involves reducing the number of children receiving school meals because they’re getting fed elsewhere (as Van Wye discovered) simply can’t be tolerated.

Welcome to the dark side, Gretchen Van Wye.