Women have no legal right to approach God
without the headship of a man.

Shocking?

Equally shocking might be the fact that:
Both men and women have no legal right to approach God without the headship of a high priest.

Leviticus 27:3-4
   ...thy estimation shall be fifty shekels of silver...
   And if it be a female, then thy estimation shall be thirty shekels.

Under the Old Covenant (Old Testament), kingship was of the tribe of Judah, and, strictly separate, priesthood was of the tribe of Levi.

2 Chronicles 19:11
   And, behold, Amariah the chief priest is over you in all matters of the Lord; and Zebadiah the son of Ishmael, the ruler of the house of Judah, for all the king's matters: also the Levites shall be officers before you. Deal courageously, and the Lord shall be with the good.

Exodus 30:10
   And Aaron (high priest) shall make an atonement upon the horns of it once in a year with the blood of the sin offering of atonements: once in the year shall he make atonement upon it throughout your generations: it is most holy unto the Lord.

Under the New Covenant (New Testament), Jesus Christ is our king of kings and our high priest by the order of Melchisedec.

Men are both kings and priests by the order of Melchisedec.  That is, kingship and priesthood are no longer separate.

And, access to God via priesthood is available to all people, not just Old Covenant Jews, via our High Priest: Jesus Christ, and our priesthood of all Christian men.

Revelation 5:10
   And hast made us unto our God kings and priests: and we shall reign on the earth.

1 Peter 2:9
   But ye are a chosen generation, a royal priesthood

1 Timothy 2:5
   For there is one God, and one mediator between God and men, the man Christ Jesus;

Hebrews 6:20
   Whither the forerunner is for us entered, even Jesus, made an high priest for ever after the order of Melchisedec.

John 14:6
   Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me.

Revelation 17:14
   ... the Lamb shall overcome them: for he is Lord of lords, and King of kings

Hebrews 5:5-10
   So also Christ glorified not himself to be made an high priest; but he that said unto him, Thou art my Son, to day have I begotten thee.
   As he saith also in another place, Thou art a priest for ever after the order of Melchisedec.
   Who in the days of his flesh, when he had offered up prayers and supplications with strong crying and tears unto him that was able to save him from death, and was heard in that he feared;
   Though he were a Son, yet learned he obedience by the things which he suffered;
   And being made perfect, he became the author of eternal salvation unto all them that obey him;
   Called of God an high priest after the order of Melchisedec.

Praying in Jesus's name:
John 14:13
    And whatsoever ye shall ask in my name, that will I do, that the Father may be glorified in the Son.

But women’s roles are the same under Old and New Covenant.
In the beginning, God gave Adam one commandment: not to eat of the tree of knowledge of good and evil.

Genesis 2:17
    But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.

Interestingly, God only gave this commandment to Adam (before God created Eve).
Eve knew about this commandment because of Adam.  Because she did not take her husband’s word as the Word of God, this began the fall.

1 Corinthians 14:34-35
   Let your women keep silence in the churches: for it is not permitted unto them to speak; but they are commanded to be under obedience as also saith the law.
   And if they will learn any thing, let them ask their husbands at home: for it is a shame for women to speak in the church.

Is this because every husband is a Biblical scholar?  No, it is because of spiritual law.  Women must approach God via the appropriate channel.  They are to submit to their husbands.

Ephesians 5:22-24
   Wives, submit yourselves unto your own husbands, as unto the Lord.
   For the husband is the head of the wife, even as Christ is the head of the church: and he is the saviour of the body.
   Therefore as the church is subject unto Christ, so let the wives be to their own husbands in every thing.

1 Timothy 2:12-14
   But I suffer not a woman to teach, nor to usurp authority over the man, but to be in silence.
   For Adam was first formed, then Eve.
   And Adam was not deceived, but the woman being deceived was in the transgression.

1 Corinthians 11:3,8-9
   the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God...
   For the man is not of the woman: but the woman of the man.
   Neither was the man created for the woman; but the woman for the man.

Colossians 3:18
   Wives, submit yourselves unto your own husbands, as it is fit in the Lord.

When the woman at the well asked Jesus for his ‘living water’, Jesus insisted that her husband would lead.
John 4:15-16
   The woman saith unto him, Sir, give me this water, that I thirst not, neither come hither to draw.
   Jesus saith unto her, Go, call thy husband, and come hither.

Vows to God:
Ecclesiastes 5:4-5
   When thou vowest a vow unto God, defer not to pay it; for he hath no pleasure in fools: pay that which thou hast vowed.
   Better is it that thou shouldest not vow, than that thou shouldest vow and not pay.

Under the Perfect Law of Moses...
Men’s vows to God:
Numbers 30:2
   If a man vow a vow unto the LORD, or swear an oath to bind his soul with a bond; he shall not break his word, he shall do according to all that proceedeth out of his mouth.

But women’s vows to God must go through her father (in her youth) or husband.
Numbers 30:3-8,13
   If a woman also vow a vow unto the LORD, and bind herself by a bond, being in her father's house in her youth;
   And her father hear her vow, and her bond wherewith she hath bound her soul, and her father shall hold his peace at her: then all her vows shall stand, and every bond wherewith she hath bound her soul shall stand.
   But if her father disallow her in the day that he heareth; not any of her vows, or of her bonds wherewith she hath bound her soul, shall stand: and the LORD shall forgive her, because her father disallowed her.
   And if she had at all an husband, when she vowed, or uttered ought out of her lips, wherewith she bound her soul;
   And her husband heard it, and held his peace at her in the day that he heard it: then her vows shall stand, and her bonds wherewith she bound her soul shall stand.
   But if her husband disallowed her on the day that he heard it; then he shall make her vow which she vowed, and that which she uttered with her lips, wherewith she bound her soul, of none effect: and the LORD shall forgive her.
   …Every vow, and every binding oath to afflict the soul, her husband may establish it, or her husband may make it void.

If men are not Christians, wives need to win their husbands to Christ, but still are under the husband's headship.

1 Peter 3:1-6
   Likewise, ye wives, be in subjection to your own husbands; that, if any obey not the word, they also may without the word be won by the conversation of the wives;
   While they behold your chaste conversation coupled with fear.
   Whose adorning let it not be that outward adorning of plaiting the hair, and of wearing of gold, or of putting on of apparel;
    But let it be the hidden man of the heart, in that which is not corruptible, even the ornament of a meek and quiet spirit, which is in the sight of God of great price.
    For after this manner in the old time the holy women also, who trusted in God, adorned themselves, being in subjection unto their own husbands:
    Even as Sara obeyed Abraham, calling him lord: whose daughters ye are, as long as ye do well, and are not afraid with any amazement.

Even if a woman is to remain single, she is to be under the headship of her father, as her father will decide if she is to be given in marriage.

1 Corinthians 7:36
    But if any man think that he behaveth himself uncomely toward his virgin, if she pass the flower of her age, and need so require, let him do what he will, he sinneth not: let them marry.

Those without male headship are of particular importance regarding care:

James 1:27
   …visit the fatherless and widows in their affliction, and to keep himself unspotted from the world.

Exodus 22:22
   Ye shall not afflict any widow, or fatherless child.

Psalm 68:5
   A father of the fatherless, and a judge of the widows, is God in his holy habitation.

Isaiah 1:17
    Learn to do well; seek judgment, relieve the oppressed, judge the fatherless, plead for the widow.

Two books of the Bible do not mention God: The book of Esther and the Song of Solomon.
Have you ever wondered why?

The book of Esther concerns the rise of a young Jewish woman, who submits to her husband, the King, and replaces the Queen who rebels against her husband.
The Song of Solomon describes the sensual love between King Solomon and one of his wives.

Both deal with the husband/wife relationship, and no mention of God exists, as that is on another hierarchical level.