Catastrophism

Catastrophism is a load of religious bullshit that essentially says, "Because of various interventions by God, there is no reason to believe laws of physics are the same as before. As a result, any dating method with such an assumption is invalid."

Historically, catastrophist was also a snarl word used by uniformitarians (geologists who equally irrationally defended the equally indefensible position that no extreme events unlike those that can be presently viewed on Earth can ever have occurred) to describe geologists who presented evidence of such events having happened, such as flood basalt flows, volcanic eruptions orders of magnitude beyond any ever witnessed in historical times, or titanic glacial outburst floods such as the great Missoula Floods.

Assumptions involved
Biblical catastrophists assume that the Book of Genesis faithfully records the history of the earth, and that therefore they have a license to dismiss all scientific evidence that does not fit in with this credo. The process is called rationalization (start with the conclusion and try to come up with explanations and evidences for said conclusion).

Other things
If the Global Flood can interfere with the decay rates (DNA decomposition or radioactive decay) of things, then one cannot deny that any other flood will be able to have a similar interference on a smaller scale. We have yet to observe such an occurrence. One of the ways to validate catastrophism would be for the creationists to come up with a recipe to produce fossils of arbitrary species in a somewhat short period of time (up to decades, because no additional global events interfere with the global rate of fossil-formation).