Killing someone to deceive your dark overlord into believing that you are their ultimate agent.
(Snape killed Dumbledore to deceive Lord Voldemort into believing Snape was his ultimate agent)
Kylo Ren needed to prove his worth to Snoke because Kylo is actually getting back at the dark side for killing his loved one, as seen by the possible grave Luke stands next to at the end of "The Force Awakens", so he Snape killed Han Solo. (This is JUST a THEORY) kylo ren severous snape dumbledore voldemortsnape killing
When you kill a loved one to prove to your dark overlord that you are their right hand man, but it is all a cover because you are an agent for the good guys.
I am snape killing my parents to show the boss I'm on his side, but I'm going to defeat him for the other side.