This passage in In Cold Blood precedes the story: "Men, our brothers, who live after us, Do not harden your hearts against us, For if you take...

Among the reasons so many were shocked and affected by the murder of the Clutter family was that the crime seemed to be meaningless and without motive. In the 1950s, the idea that a person or people would kill someone for the thrill was incomprehensible and a clear indication that the person who committed the crime was a monster. In light of that, one of Capote's objectives was to demonstrate that, despite the violent and...

Among the reasons so many were shocked and affected by the murder of the Clutter family was that the crime seemed to be meaningless and without motive. In the 1950s, the idea that a person or people would kill someone for the thrill was incomprehensible and a clear indication that the person who committed the crime was a monster. In light of that, one of Capote's objectives was to demonstrate that, despite the violent and shocking nature of the crime, the murder wasn't the act of a monster, but of an ordinary human being. Moreover, Capote largely avoids the good/evil binary, choosing instead to explore how the personal history and experiences of each killer has led up to the murder of the Clutters.

When it comes to his portrayal of Perry Smith and Dick Hickcock, his bias is heavily present throughout the story. In describing Dick, Capote is generally light on sympathy and at times seems to go out of his way to emphasize Dick's violent and psychotic behavior. His description of Perry, on the other hand, is almost overly sympathetic. Capote spends considerable time detailing Perry's tragic personal history, pointing out the various ways in which he has been victimized and abused in his younger years. While he never tries to justify the behavior of either man, it is apparent that Capote sees (and wants the reader to see) a possible connection between Perry's personal history and his crime, which has provoked the author's sympathy. He offers considerably less sympathy for Hickcock.

As for the Villion quote that appears at the beginning of the story, you are correct in connecting it with Capote's desire for the criminals to be better-understood and forgiven. From his perspective, the violence and abuse that Perry suffered as a child has led to his violent behavior. Therefore, to offer  compassion, pity, or forgiveness has the potential to break those cycles and possibly prevent such things from happening in the future.