Interpretation of the confession (major spoilers)
Ok I really like this movie. Gave it a 8/10. Now as to Hearsts false confession and this is just my own opinion on this, as there is room for viewer interpretation due to the ambigutiy of the ending.
I think his false confession was a sort of "Well *uck you then." to his wife. The entire storyline revolves around their marriage even though these murders are the focus of the film. As everything plays out through the Q&A regarding the murders the constant theme is the state of their now dysfunctional relationship. It all stems from her lack of trust in him at the Christmas party and downward spirals from there. Her lack of trust and his disappointment that she should know him better causes him deep pain as only true love can. He has pretty much loved and cared for her, her entire life and now he feels betrayed that she would even consider him guilty of this crime.
So he just gives up because he is basically all used up and has given up hope for them. In his mind he thinks "OK if thats what you think I am then I will be what you think." I know its a kind of self-defeating logic but havent you ever felt that way? Ultimately his intent is to hurt her back they way that he feels hurt.
There is, NO Gene for the Human Spirit. Gattaca