You know, I'm an old fashioned kind of guy so I'll try to explain what I think from two angles. The first is a single woman and the other is a married one.
THE SINGLE WOMAN: As a single lady, you are supposed to be self-reliant in every single way. In life there is only one man that owes you anything and he is your father. He birthed you and as such you are his responsibility until you grow up. Beyond that you are an adult and should be able to provide for yourself. The same applies to your mother. So as a single lady, no one owes you anything and you owe no one anything. Thus you should rely solely on yourself for anything you need.
THE MARRIED WOMAN: When we talk about married women, my old fashioned way of thinking comes in. As a married woman, I feel you should be totally dependent on your husband. I'm more of a man-goes-to-work woman-raises-kids kind of guy. Not because I believe that women are slaves to their husbands. No. I believe so because I know that a marriage is a partnership. Both parties have roles to play. When a man makes his vows at the alter, he promises to provide for his wife. It is his matrimonial duty to provide for her and the kids. Its not an easy job. Neither is raising kids. I think the problem we have today is because people no longer appreciate how hard it is to raise children. Its a tough job but it is necessary. So in a family, the man goes out works and pays the bills. His wife takes care of the kids and manages the home. Both jobs are hard. Both jobs are necessary. So only in this situation can a woman not be self-reliant. Because she leaves the duty of providing for her husband and focuses on other things. That's what I believe and that's how I feel about women being self-reliant