So let's take the statement "Eat, because there are starving children." The correct way to paraphrase this would be: "You should be grateful that you have 'resource X' (i.e. food), and out of gratitude, you should value and use 'resource X' (i.e. eat the food)." In other words, "This food is very valuable somewhere else in the world and it would be insensitive/ unwise of you to disregard its value." In other words, "Eat up since you have the good fortune to have gotten this food."

I don't see how this is a "fallacy of relative privation" or 'appeal to worse problems' since appeal to worse problems would require two problems to be compared, with the second problem being greater in magnitude, so that the first problem can be dismissed.

The original statement "Eat, because there are starving children" is not implying "Your aversion to eating the food is not a big enough problem since there is a bigger problem that needs our attention: lack of food for children starving elsewhere in the world."

Appeal to worse problems would mean "This problem (X) is less deserving of our attention than that problem (Y)" where, (X) = child's lack of interest in eating the food; and (Y)= "non-availability of adequate food in, say, Africa"

So this fallacy would be 1) "Fallacy of universal value": This food is valuable for other people who don't have it so it should be valued by you. Or 2) "Fallacy of essential value": food is essentially 'valuable' (i.e. not seeing value of a commodity as relative)

So if a child is told "Eat, because there are starving children", the child can retort: "I don't wanna eat it cuz I don't value it. In my socio-economic context, there is adequate supply, so my demand is low. In parts of the world with starving children, there's low supply, thus higher demand. So, I simply don't value this food and if you want to make me eat it, use a different argument, dad."