I always thought that Arcturus wanted Kerrigan to die on Tarsonis, since she was the assassin that killed off his father and mother during the first Korhal uprising (she was conditioned at the time). He figured that the Zerg will do the job, never expect the whole infestation to take place.
I think the the "his greatest failure" part comes from the fact that Arcturus had several earlier opportunities to take down Kerrigan, but never took it. At that point, it is checkmate one way or another. The swarm was already devastating Korhal and Kerrigan was the only thing that is preventing the swam from pulling an Aiur, post-overmind death.
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