Feminism, as it is defined, is the "advocacy of women's rights on the basis of the equality of the sexes," according to the Merriam-Webster dictionary. This is NOT where the problem lies.
Eve was made from the rib of Adam, not from the foot to be below him, or the head to be above him, but the rib to stand beside him. The problem does not stand with the ideology that women and men are equal as humans, as this is a Biblical truth.
The problem lies within what feminism has become.
For Christian women, our calling is outlined directly in Titus 2. It states, "(women) are to love their husbands and children, be self-controlled, pure, working at home, kind, and submissive to their own husbands."
This seems to fly directly in the face of modern feminism, doesn't it? Working at home?! How dare you say that! Notably, this verse never says women cannot have a career outside of the home; it simply says that the home is a priority when a woman has a husband and children.
Submissive to their husbands?! That sounds like slavery!
The church is to submit to Christ's word and will, and the husband is to be the spiritual leader of his home. Similarly, the wife is ideally like the church in which she allows her husband to lead the family. It never says that a woman is a servant and can be abused by her husband.
Modern feminism teaches that women are not just similar to men, but that they should be better.
They constantly focus on what they can do that men can't, and what they can do better than men. Why is this a problem for Christian women? Men and women are meant to complement each other in their personalities and physicalities, they are not meant to try and outdo each other.
God made both man and woman to bind together and live life together, as humans are made for companionship. Modern feminism also teaches that you have every right to abort a child within you, even if it's a result of your own irresponsibilities.
Jeremiah 1:5 states, "Before I formed you in the womb, I knew you. Before you were born, I set you apart..." As a Christian woman, how could you support an ideology that completely disregards the sanctity of human life?
Modern feminism attacks the core of Christian womanhood and effectively destroys the special qualities of women created by God.
We are made differently than men and that is OK. If you are a Christian woman, and you hold the truths of the Bible as law in your heart, there is absolutely no logical way that modern feminist ideologies can coexist.