ST Importance of Killing a Family Member

Did a search and didn't find anything on this. So my apologies if the discussion is already in another thread.

I wonder about the importance of striking down a family member. If memory serves me correct, Kylo is the first we have seen do this, and it seemed rather significant. Luke could not strike down Vader, but instead surrendered his light saber saying he will not succumb to the dark side. I haven't seen ROTJ in several years, but I remember the Emperor telling Luke to strike down his father and fulfill his destiny.

Vader couldn't sit by and watch the Emperor kill Luke either. Family was always important to Annakin/Vader. In fact, this type of attachment was part of his downfall.

While we don't know for certain if Kylo killed one of the KOR to protect Rey, if this does hold to be true and Rey is part of Kylo's family, it could be evidence of one of his weak moments. A weakness he finally put to rest by killing his own father. After striking down his father. Snoke mentions it is time for Kylo to complete his training. I wonder if we will see a new level of the Dark Side in Kylo now that he has completed this task. Kind of the ultimate submission to the Dark Side.