Here's why:
* Genetic Trace: Jerome's brother, Anton, finds the hair and uses it to trace Irene's identity. This discovery is crucial because it allows Anton to identify Irene as the woman Jerome has been seeing.
* Revealing Jerome's Secret: The hair, along with the other evidence Anton finds, leads him to the truth about Jerome's identity and his relationship with Irene. This sets in motion the events that will ultimately lead to Jerome's exposure.
The seemingly insignificant hair plays a key role in the plot of Gattaca, highlighting how even the smallest details can have a significant impact in a society obsessed with genetic purity.