Saying that a human being is incapable of overcoming a huge mistake in life is antithetical to our American experience. Our entire justice system is based (presumably) on the theory of rehabilitation. If you can presume a sex offender is incapable of change, then you cannot likewise allow for anyone who committed a crime to change.
How much different is the drug-user, drug-dealer, murderer, alcoholic, drunk driver, thief, animal abuser, or wife-beater? Any one of these offenders could be seen as unable to change...but our justice system and nation's history has always been all about giving them a chance to change. And we do. The bias against one group of people is insane and irrational.
One gross mistake in life is hardly a reason to throw away a human life in this country. And those with the personal biases and prejudices who advocate hanging sex offenders who have served their time are nothing more than those who want minorities hanged from trees.