A woman is never always dependent. She's dependent for as long as a man is dependent on her.
The situation of womanhood in my country (India) seems to be improving. Women are working on higher posts in top companies than they used to, they're opening up and share their views in public, they're doing great in sports, they're as good as men in every field. These women aren't dependent on their father and husband for sure. Not financially atleast.
When for years and years, our society has been a male dominant one than automatically women will feel dependent. When they're not allowed to work, share their thoughts, are considered impure when they're on periods, can't share what they feel about certain things, aren't allowed to go out in the evening or dress up the way they want to, their opinion does not even exist. You're basically making a person feel that he/she has no worth. They're born only to be married to someone and then cook for the in-laws and new family for life. How do you expect someone who was never allowed to speak or do anything willingly not be dependent on her husband or father?
For someone to be independent you also should stop making them feel worthless and start valuing them equally.
Women who are homemakers work all the day and much more than men. They wake up before anyone else in the house and sleep after everyone is asleep. They work everyday and all the time with very little rest. How many of these men who go to office know how to cook food? How many of them wash their own dirty stinking clothes? Taking care of a house and everyone living their, is not easy, my friend. If you look at it from where I am looking, men are more or less equally dependent on their better halves.
Things are changing. A LOT of change is still NECESSARY.