The second broad category is sometimes called "heavy-metal dating," and includes Uranium-Thorium-Lead, Rubidium-Strontium, and Potassium- Argon systems.
These are the methods that are commonly used on inorganic samples such as rocks, and that often give extremely long ages-millions or billions of years.
Reasons given usually involved detrital intrusion, leakage or leaching of some of the isotopes in the sample, and sometimes the initial isotopic content of the sample.
For K-Ar dates, it's easy to blame argon loss if the reported age is too short, or argon absorption if it's too long.
Of course, the fossil dates depend on the assumption of evolution.And, of course, the public doesn't usually hear of these wrong answers.This statement - that radiometric dates are "corrected" by reference to evolution-based index fossils - is hotly contested, but examination of the technical literature shows that it is true, in spite of what elementary textbooks say. Documented Discrepancies The general public believes that radiometric results are consistent and thus demonstrably reliable. John Woodmorappe did an extensive literature search, looking at 445 technical articles from 54 reputable geochronology and geology journals.1 These reports listed over 350 dates, measured by radiometric methods, that conflicted badly with the ages assigned to fossils found in these same strata.Studies have been made of submarine basalt rocks of known recent age near Hawaii. Yet it was found beneath a layer of the volcanic KBS Tuff that had an accepted radiometric date of 2.6 MY (millions of years old).Leakey declared that the skull was 2.9 MY, and said that it "fits no previous models of human beginnings." It was named KNM-ER-1470 (for Kenya National Museum, East Rudolf, #1470).Most people, even the experts in the field, forget the assumptions on which radiometric dating is based.