Why don't women compete on the pommel horse in gymnastics?

When artistic gymnastics was developing into the sport it is today, men and women had more traditional and fixed gender roles that were reflected in the skills chosen to be emphasised in the different apparatuses. For men, upper body strength was a crucial factor, while for women, accentuating the grace and beauty of the slim feminine physique was preferred. Each apparatus places different demands on strength, and the pommel horse is particularly strength-based. Keep in mind that in this era, women were also seen as intrinsically less physically and mentally capable of the same tasks as men.

The gender split in apparatus options fluctuated initially, but as time went on, the differences became crystalised into the current traditions and rules of the sport, and as a result there is a lot of inertia to change. It's a bit of a chicken and egg problem - women would be capable of doing the pommel horse these days, but without any competitions, role models or incentive to do so, they are more likely to train for the more artistic apparatuses available and not demand competitions with the pommel horse.

https://www.jezebel.com/female-gymnasts-used-to-compete-on-the-rings-but-the-game-changed