As it says the 'difference in incidence was small.' In this case it is only a very small tilt towards women in the younger age ranges. The lower age ranges less people have had the jab and more women are likely to have. Being more likely to be health care workers or home cares etc. Something like 3 women for every 2 men. Hardly a womans problem if a good percentage of men get it too. More data is needed before any should be saying this is a predominantly women issue. The numbers so far show men take up a large chunk too.
Also risks are still rare with the vaccine compared to other life choices we make. If the virus cases were still high they would not be changing the schedule. It is a weigh up of our current risk in each age range.
On the question of the pill. I believe the EMA have looked into that and ruled it out. Though that was a few weeks ago now. I have no idea about the latest idea on it.