the worst insult you can throw at somebody today is “you’re a child”. because in the minds of the US citizen, the child is the worst things in existence. schools exist to quarantine them, to remove them from society, to make them “proper” humans, adults, in other words.
the reason why the child is considered the most despicable object in US mainstream culture is because the child represents nature, the thing that is a direct offspring of biology, instinct, and whatever we consider “uncultured uncivilized being”. in the US, the child is like a piece of dirt, or clay maybe, that has to be sculpted and burned into porcellaine before it’s considered worth anything. even more, the child - through its playful instinct and lust for life - might even represent the animal instinct that has been so successfully repressed in every Grown-up human. and we cannot accept what was never accepted about ourselves.
I’m not familiar with that show, but I see what you mean. Usually; when someone says ‘you’re a child’ I find it means they aren’t thinking of a bigger picture, or sometimes that they are being selfish. The panicking the other character does is kind of strange. On the other hand, there are lots of bits of media with the idea that children are wonderful, and whimsical, and have a joy that many have lost as they age.
All this said, media or not, people in the US are probably quite similar to the people you know. Just people who want to live their lives, and for many they dream of having a family, and kids. I don’t think I know anyone who hates children, but I do know many people who have kids, and they are loved.