Is the Bible against women?

Not at all. The Bible commands husbands to love their wives as a rule, in the highest terms it has:

Husbands, love your wives, even as Christ also loved the church, and gave himself for it;

How many husbands would give their lives for their wives? That is the standard Scripture sets for how a woman is to be treated.

So ought men to love their wives as their own bodies. He that loveth his wife loveth himself. For no man ever yet hated his own flesh; but nourisheth and cherisheth it, even as the Lord the church:

Before Christ, equal

In Christ, there is no distinction in worth between men and women:

There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus.

In marriage, a woman is not given to her husband as property - the two become one flesh:

Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh.

Trusted as witnesses when the world would not trust them

The Bible uses women as the first witnesses of Jesus’ resurrection - at a time when a woman’s testimony was not even accepted in a Jewish or Roman court. The risen Christ appeared first to women and sent them to tell the men:

Jesus saith unto her, Touch me not; for I am not yet ascended to my Father: but go to my brethren, and say unto them, I ascend unto my Father, and your Father; and to my God, and your God.

The Gospel writers had every cultural incentive to invent more credible witnesses if they were inventing the story at all. Instead they recorded what happened: women were first at the tomb, first to see Him, and first entrusted with the news.

What about the household order Paul describes?

Scripture does set out an order within marriage, and it is often read as though it demeaned women. Paul describes it this way:

But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God.

Notice the pattern: the headship of Christ over the man is the same kind of headship Paul has in view for the man over his wife. Christ, though equal with God the Father, willingly placed Himself under the Father’s authority without ceasing to be equal in nature and worth. A wife accepting her husband’s headship - not women in general, and not as inferiors - follows that same pattern, while the husband is commanded to love her as Christ loved the church and gave Himself for her.

Saying the Bible is against women because of this is like saying God the Father is against Jesus Christ, the Son He sent and loves.