I'm not saying that Bergner's actions: killing Nabi and attempting to silent Kibi, are right, we all know being a mafia is not considered a good thing anyway. I think Bergner just wanted to play it safe. Like
@lexy mentioned, Anna's father is like a mafia boss and, imo, as the head of bodyguards protecting Anna, Bergner has to kill Kibi, who's obviously very close to Nabi, to prevent Kibi from growing up, learning about Nabi's killer, and planning to avenge for Nabi. Who knows what will Kibi do? He could try to hurt their most important person, Anna, by teaming up with some other powerful group, who might be even more powerful than Anna's and we still yet to learn about up till now. He might become friend with Anna since they're close in age, and he will definitely be close to the other members - considering his natural friendly nature. Everyone's going to get hurt, physically and mentally. However, Bergner's not cold-hearted enough seeing he faced anxiety after killing Nabi, he decided to listen to Kibi's will first.