Parsimony seeks the simplest answer, but high rates of evolutionary change, especially at the DNA level in noncoding regions, make for many, many characters which must all be aligned to derive relationships. A limited number of character states means that characters can evolve in parallel repeatedly, confusing the search for the simplest answer to an evolutionary sequence.
Work Step by Step
First look at the definition of parsimony and then try to imagine how lots and lots of changes (a high rate of evolution) or a low number of results/character states could confuse this. The first is like trying to figure out which set of footprints show who came into a room first when there are 100 sets of footprints while the second is like trying to figure out who committed a murder based on a footprint found at the crime scene if there are only four kinds of shoes sold in a city of a million residents where the murder took place.