Is it true that a woman's identity in society is only on account of her relationships with a man?

So would you have no identity if you were not someone's daughter, sister, wife, mother?

Also is it true that most women dont want an identity apart from an identity from her relationship with her man?

On the other hand, why are men not defined by their relationships ? and why are they defined by their status and position in society?

And why is it that when either a man or a woman tries to break away from the mould (such as a man becoming a house husband or a woman becoming a career woman) the society just berates you?