What was K talking about?
About things J shouldn't know, and why shouldn't J help K fight Boris.
In his apartment K got a weapon from his hidden collection, and was taking a defensive posture with it, as though he was expecting Boris to come there and try to kill him. He doesn't seem to know that Boris can or will travel back to 1969 to kill him and prevent the ArcNet.
Is he expecting to die in the present time frame? Is that what's bothering him? And his mention of regret on the phone, was that referring to not killing Boris the first time?
Was his anger and insistence that J stay out of the Boris fight because he thought Boris would kill J also?
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The story is king.