I can see you are extremely emotional about this issue.
I doubt the opposition to feeding children is based on some "out group" bias, but more in the practicalities. The argument is two fold; quality and cost. Free food for children will prompt more parents to simply rely on the government to feed their children, resulting in worse health outcomes for the children. That's the quality argument, and it's not a bad one truth be told.
Cost is, of course, as I mentioned; I have yet to meet a government program which didn't try to grow their budget while providing the least possible to fulfill their job function ( and, federally, often failing even in that ).
Mind you, none of this considers the secondary impact of free food. Probably the most obvious to me is the creation of food deserts; small grocery stores just barely hanging on which then lose this source of income, shutting down.
Giving things away always have some pretty gnarly consequences that should be heavily considered. But no; it's all about emotion: "Starving children!", and all logic and sense fly out the window.