My impressions, at best when it came to killing Harry, Kincaid was a reluctant assassin. He understood why Harry wanted him to assist his suicide, he respected it, so he agreed.
Of course Ivy also knew and understood, she loves Harry as a friend, but the Archive sees the big
picture. The Archive knows where Harry fits in the big picture and the lessons he has to learn. So
it came up with the compromise, head kill, instant death or disability beyond even Harry's ability to heal from. Chest wound, if he falls right [which somehow was managed] he'd come very close to death, but survive.
Ivy also understands that Kincaid has paternal feelings for her, and in her own way she does see him as a father.. However the Archive knows it must distance itself and her from humanity now, least she go mad, so she sent Kincaid away, she and it must be on her/it's own now. But it wasn't easy, I bet it is the last tears we ever hear of Ivy ever shedding for anyone.