First of all, let me start off by saying that you can agree with and fight for women's rights without being or calling yourself a feminist.
Feminism (noun): The advocacy of women's rights on the basis of equal rights
I do not agree with men being treated better than women. There is no excuse for treating women poorly or unfairly. But, I believe that men and women were not actually created to be equal.
God made men to be the higher beings but that does not mean the better beings. That also doesn't mean that men are favored over women. God made men to be the head of households. God made men to care for their wives "just as Christ loves the Church."
"For the husband is the head of the wife even as Christ is the head of the church, his body, and is himself its Savior " - Ephesians 5:23
Women should lift each other up. Women should empower each other. Women have power and purpose and can do marvelous things not only in society, but for the Kingdom of God which should not go unnoticed or ignored.
People can tend to get so locked into the idea that God created men to be the head of household and care for their wives but forget that God made Eve for Adam (Then the Lord God said “It is not good for the man to be alone. I will make a helper who is just right for him.” Genesis 2:18). The woman was made for the man, therefore the man's role was formed to lead the woman. The man leads the woman not in a strict or abusive way, but in a way that helps them both grow spiritually and in their relationship. Now, don't get me wrong, a woman can totally play a vital part in that said growth - it's not a bad thing. Yet, man was formed first and think of it as the man's duties/offering to God for creating women for the man.
This can get twisted. Women, you are not a man's property.
Taking the Bible out of context and using the fact that God created woman for man does not give men any excuses to treat women like they are a piece of property or slaves. That is not God's intention. Man and women are made for each other, both under Christ.
As a final note, I will end with the fact again that God does not show favoritism (Romans 2:11).
God created and formed both man and woman and loves both equally. It is our roles that are not equal. We don't always know why God does what He does - but we know that it is for good - our good.