Also see: Were There Women at the Olympic Games?
Here are my thoughts:
- Women were second-class people, like slaves and foreigners. Only free-born Greek (male) citizens were allowed (at least until the Romans began to exert their influence).
- It is likely that women were considered a pollutant, like women on ships in more recent centuries.
- Women had their own games (Hera games) starting in the 6th century where they competed dressed.
- Olympic performers were naked and it would have been unacceptable to have respectable women performing naked in mixed company. It may have been unacceptable for respectable women to view naked male bodies of non-relatives.
- There could have been a risk of touching sexually-charged body parts. Not a problem for prostitutes.
- Athletes were required to train for 10 months -- a length of time most married or widowed women probably didn't have free.
- The poleis (city-states) were honored by an Olympic victory. It is possible that a victory by a woman would not be considered an honor.
- Being defeated by a woman would probably have been a disgrace.