This is because of the legal basis of the American criminal law system. Most crimes in the United States have an actus reus -- a guilty act -- and a mens rea -- or guilty mental state. For example, the New York Penal Code defines second-degree murder as causing the death of a person (guilty act) with the intent to cause the death of a person (mental state). N.Y. Penal § 125.25(1) By contrast, second-degree manslaughter is defined as causing the death of a person (guilty act) recklessly (mental state). N.Y. Penal 125.15(1).
The diminished capacity plea is based in the belief that certain people, because of mental impairment or disease, are simply incapable of possessing the mental state required to commit a certain crime. In the example of murder and manslaughter, diminished capacity states that a certain defendant is incapable of intending to cause a death, and therefore must have at most caused such a death recklessly. Thus, a successful plea of diminished capacity in a murder trial would likely result in the charge being reduced to manslaughter.
White's attorneys argued diminished capacity. They claimed that a diet of only junk food had created a chemical imbalance in White's brain (the "Twinkie defense"), and that he was depressed over his loss of his city supervisor position. Therefore, he was unable to premeditate murder, one of the requirements for first-degree murder.
The jury convicted White of voluntary manslaughter -- the least serious charge for homicide. This caused an uproar against the diminished capacity plea in California, and in 1982, voters overwhelmingly approved a proposition to eliminate the defense.
The USSG sets minimum sentencing for certain federal crimes, and also sets the guidelines by which judges may stray from these minimums. The USSG states that a federal court may depart downward from the minimum sentence on the basis of diminished capacity if the offense was nonviolent. U.S.S.G. § 5K2.13. See also United States v. Cook, 53 F.3d 1029 (9th Cir. 1994). However, this doesn't apply in Kaczynski, since the defendant is being accused of a violent crime.
U.S.S.G. § 5K2.0 allows departure from the sentencing minimums for "extraordinary mental condition." Unlike 5K2.13, this section does not explicitly limit the departure to non-violent crimes. However, it was not until very recently that the Court of Appeals for the Ninth Circuit explicitly recognized that 5K2.0 creates a "diminished capacity" argument for violent crimes.
In United States v. Green (9th Cir. Sept. 8, 1997), the Ninth Circuit ruled that the trial court had the discretion to depart downward in sentencing based on diminished capacity in the case of the defendant, a man who pled guilty to two counts of bank robbery.
A successful plea of diminished capacity would not earn a "not guilty" verdict, but merely a reduced sentence, under the federal sentencing guidelines.