Having a child predecease you is one of the worst things that can happen to a person in general. This is a common sentiment in humans. The strange thing is that you mentioned you're trying to follow "logic." This is not logic. These are emotions.
> the idea of being told my 1 week old baby is going to die
not
> the idea of my child dying
> my baby is going to die, woe is me
and more of
> have I failed my baby so much as a parent that he won’t even grow to adulthood (much less have a wonderful, happy life)
It’s not exactly a rational feeling; it’s not like this baby was going to die through lack of parental effort or care or anything else that the parents have any real control over, so it’s not like they could have done anything differently.
Nonetheless, it can make you feel like an utter failure of a parent. To some people (I admit, not everybody), that is absolutely crushing.
It only looks irrational if you don't understand what people and feelings are.