Because people thinks it's utterly ridiculous, doesn't mean it's "touched a nerve". It means they think it's utterly ridiculous.
Not having access to a parent 100% of the time shouldn't default to feeling rejected. And if a child does feel that way, it's because a parent has made them think it's unfair, because it's not an unreasonable thing at all.
Similarly, a child should understand that if they spent 100% of their time in one household, they would do (pretty much) 100% of things in that household. And if they spend, say, 70% of their time, then 30% of their time over two households, that (pretty much) they would do 70% and 30% of the things in those respective households. And this shouldn't cause a child to feel rejected, that's what happens when their parents don't live together. And it's on the parents to make the child understand this.
"You have to go to school, remember" shouldn't cause feelings of deep rejection. "Mum/Dad will be away this weekend, but they can't wait to see you next weekend" as a one off, shouldn't cause feelings of deep rejection. "It's a week of doing baby things, and you'd be bored stiff" shouldn't cause feelings of deep rejection. Maybe the non resident parent can only afford a term time break. A child may be naturally disappointed, but it can be handled two ways. A simple explanation as to why they aren't going (predominantly the fact they're in full time education) so they understand that they couldn't go. Or, you could tell the child "well, I would let you have the time off school, so there's nothing stopping you going" which is fueling the child to think the only good reason they aren't there, is because they aren't wanted. It all depends on how the parents present this to the child.