Why does Porfiry Petrovich talk at such length about the proof that psychology offers the painter guilt and why he urge Raskolnikov to confess?

If he were to play the part of the average policeman or criminal investigator and concern himself only with trapping the criminal immediately, Porfiry would have arrested Raskolnikov very early in the novel. But Porfiry's aim is not so much to see the criminal locked behind bars as it is to help rehabilitate the criminal and make him into a useful member of society. Therefore, in the final interview, Porfiry gives Raskolnikov some more time in order to confess because a free confession would mitigate the sentence.

Through all of their interviews, Porfiry shows himself to be one of the advanced thinkers of Russia through his use of psychology and new methods, and his belief in the possible rehabilitation of criminals into useful members of society.