Voldemort intended the object to be used by his most loyal follower in the event that his horcruxes were destroyed, but it ended up in Hermione's possession instead. She knows she has to kill him. Steal his horcruxes. Destroy him. But Tom Riddle isn't who she thought he was. Hermione discovers it's a dark descent into the madness of the man she should hate, but can't. When she realizes Tom Riddle's soul is half of her own, she knows she can't destroy him. To kill him would be to destroy herself. There simply has to be another way.