meringue, just responding to your points:
"To me being a woman means being strong, resilient, intelligent, empathetic, non violent, caring for others and the environment. I know that many men have these qualities too of course, but for me they are innately associated with womanhood."
i don't think you can say these things are innate. for many women these qualities socialised or forced into them, and these things are so ingrained that it is impossible for us to know how women would behave without it. for some they will come naturally, for others they will perform the behaviours because it what is expected of them, others will actively resist and be deemed bad women (not bad people; bad women). it's very dangerous to say that they are innate, because what of those women who struggle to exhibit those qualities? are they not women too?
and to extrapolate, you are suggesting that men who do display those qualities are what? not men? woman-like? how do they otherwise come to exhibit these behaviours if they are innately associated with womanhood?
"Some of the PP seemed to suggest that "being a woman" was defined only by the experience of oppression. This seems a bit depressing and limiting to me - would you say the same about being black or Jewish for example?"
women's behaviours that are often perceived as "innate" may well be the result of oppression. if the majority of women are living in fear of male violence directed at them on a daily basis (not necessarily a blatant threat, but the violence of other men is enough for many women to treat all men with caution) how do you think they might adapt their behaviours? might they become more "strong, resilient, ... empathetic, non violent, caring for others" in order to decrease the likelihood of attracting male violence? it is limiting - that is the problem, and that is why we have feminism
i can't speak for black or jewish people of course, but it wouldn't surprise me if someone from those communities said that they altered their behaviour among white or non-jewish people as a result of socialisation and the long history of oppressive and violent behaviour. (and as an aside, my jewish friends tell me that the concept of exodus is fundamental to jewish people's sense of identity, though please do correct me if i have misrepresented this)