What is Dostoevsky's argument for why Raskolnikov was wrong?

Spoilers for Crime and Punishment:

In Crime and Punishment, it's quite clear Dostoevsky is trying to convey the idea that Raskolnikov murdering his landlady was unjust. He does this by having Raskolnikov go through serious mental anguish and torment after the murder takes place and eventually Raskolnikov confesses his sin and chooses to repent by going to jail.

But is this really an argument against Raskolnikov's ideology, one which seems to argue via utilitarianism that his actions were just? What are the actual, logical arguments against Raskolnikov's reasoning?

Or is Dostoevsky trying to say that there is no rational logical reasoning behind morality, and that the only way to counteract it, the only way to act good is accept that goodness is God-given, and what is "right" cannot be rationally arrived at, it needs to be realised in some sort of spiritual awakening?