It seems, and I can imagine, Alice is troubled and broken by her past experiences. Let's not underestimate negligence and the consequences.
'I want to kill Karan' is more or less a statement of feeling powerless. Since KV is pinpointing the truth once again, it is hurtful for her and it is difficult for her to accept those words. She is focusing on the wrong points and tends to stay in that zone too long.
Hope she can change this about herself around. She actually needs someone like KV. A (kind or harsh) mirror which she can use for her own improvement.
I am sure she will have a conversation with KV about it at some point because this will annoy her mind.
KV did well in the tandav room. Though, he booted out Shrutika to early. Loved he did not 'kick' them out.