On the one hand, I can understand the desire to leave the Hiraizumi monster alone in order to protect the feelings of those close to her such as her friends and family, on the other there's the concern that at some point the Hiraizumi monster will also self-propagate and will hurt the people around her (Such as again, her friends and family)
So I think in this instance, I lean a bit more on Itou's side, in getting rid of the monster.