why do people feel more sad when their child kills themselves

First of all I'm pretty damn sure it's a horrible feeling if your child causes the death of others. It is just less socially acceptable to speak out about it because the entire world kind of wants you to shut the fuck up if you helped creating the person who became a killer. You are in many cases blamed at least partially. And even disregarding that, you'll just have lots of conflicting feelings. People do not typically stop loving their child just because they do something artrocious. The love between a parent and a child goes deeper than any kind of rational argument. It just is. And no one is wanting to hear from someone who loves the killer after it happened.

As for why suicide is so bad, because parents will forever wonder whether they could've done something, could've done more. This is also the case in the above scenario but in case of an accident or a disease it is much less plausible that they could've actively prevented it from happening. Another factor is that loved ones are often blind-sided and on top of the grief realize that their child suffered alone and they never knew. That is a terrible powerless feeling.

Last but not least, talking about wanting to kill people out of frustration is fairly common and a stupid fucking thing to do if you actually plan on killing anyone (unless you're already prepared to follow them into the grave). Whereas cries for help before an actual suicide happens are common.