Hamada-sensei was backed up, and I mean that literally, this man is not shy about his proclivities.
This manga is entirely his outlet for his craziness, and I respect the hell out of him to still have done a good story with it.
I think what Susuzumi meant with that was... that what they want from Sunao is that she will entirely accept that she is killing a person but not see it as an obligation but a duty that needs to be carried with subtlety.
By just looking at it as "cutting him down" she is washing her hands of any guilt, and they don't want that, they fear that if they lose that "guilt" they could get too used to the act of killing and see as just anything else... which could lead them astray, but at the same time if they let guilt consume them they would be unable to keep going or go crazy.
It is a delicate balance, but one that needs to be achieved and maintained.
They are using powers that are connected to their souls, a connection that they themselves don't entirely understand but know that if taken lightly can bring disaster.