Short answer:  I have no idea.

Longer answer:  Really, I have no idea.  And as far as I can tell, neither does anyone else, beyond speculation.

But the difference in susceptibility is real:  here is one study performed at Kaiser Permanente, showing that men have almost double the risk of developing Parkinson’s:

Incidence of Parkinson’s Disease: Variation by Age, Gender, and Race/Ethnicity

Other studies seem to have found a somewhat smaller gap, but still significant (~50%).  Race/ethnicity appears to play a smaller role, but possibly some significant differences.