Ask that question of a feminist and he would say it's because the Bible is
the product of male chauvinists. But the true answer indicates a profound
and logical chain of authority that emanates from God the Creator. The
human race (collectively known as man) was created male and female for
purposes of an earthly existence. This is seen in Jesus' answer when the
Sadducees, arguing against the resurrection, presented a hypothetical case
of a woman who had seven husbands, (Matt. 22:23-30). He pointed out that
male and female constitute an earthly arrangement. The whole is
comprehended in the two genders which serve to procreate the race. But
that need passes with the passing of things temporal.
"And God said, Let us make man in our image, after our likeness...So God
created man in his own image, in the image of God created him; male and
female created he them. And God blessed them, and God said unto them, Be
fruitful, and multiply, and replenish the earth, and subdue it...," (Gen.1:26-28).
God said "let us make man" and then proceeded to create two genders in His image. God "created man in his own image, in the image of God created he him; male and female created he them." Now, which is it? Did God create him or them in his image? Man in this passage is the antecedent of both him and them. The female is comprehended in both terms. Man is dual. As he is body and soul, so he is male and female and God intended for authority and leadership to reside in the male. The existence of two sexes is for a purpose and that's the same purpose Jesus expressed in his answer to the Sadducees. The relationship of male and female ceases at death. In the resurrection there will be neither. We will be as the angels of heaven.
There is a Biblical chain of authority which explains why Jesus wasn't a woman. That chain of authority is expressed by the apostle Paul in his first letter to Corinth.
"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." (1 Cor. 11:3)
God, in whom authority inheres and resides, has given all authority to Christ, (Matt. 28:18) Man is under Christ and woman is under the authority of man. Male and female are sub-divisions which complete the whole of man. While Christ entered the world through the agency of a woman, he came as a man because of his authority. Paul says the male was created first, and by virtue of this, has authority over the female in the earthly arrangement of things, (1 Tim. 2:8-13). Deity tabernacled in the flesh of man which is a synecdoche for both male and female and lived as a man in whom human authority resides.
Feminist rantings notwithstanding, this is the Biblical chain of authority. Male and female are comprehended in the term man in Genesis 1 and the apostle Paul offers an inspired commentary on the Genesis record his first Corinthian letter.
"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...Nevertheless neither is the man without the woman, neither the woman without the man, in the Lord For as the woman is of the man, even so is the man also by the woman; but all things of God." (1 Cor. 11:8-12).
While the woman was created for the man, he enters the world through the woman and both were created in Adam. Male and female characteristics inhere in both men and women. Sharing both estrogen and testosterone, men and women constitute the whole of man. But the male is the one in whom God has reposed authority and while Christ was on earth he had authority over the demonic world (Matt. 12:22), disease (Matt. 15:30-31), the elements (Mark 4:38-41) and death (John 11:43-44). As the firstborn son of Mary he also held and exercised authority and responsibility in committing the care of his mother to John, (John 19:26-27)
Christ's authority precluded his advent as a woman. Women were given no authority as apostles in the transmission of truth (John 14:26; 16:13; c.f. Acts 1:2, 13), nor were they given authority to preach the gospel, (1 Tim. 2:8-15). While they were and are called to be His disciples, they have no authority to lead or speak in the public assemblies of the church, nor to serve as elders, (1 Tim. 3:1-2). When Paul issued his apostolic injunction against women usurping authority over men, (1 Tim. 2:12), he was inspired to select the word aner (aner). That word was used to specify a male only as opposed to "anthropos" which means mankind.
Christ entered the world and dwelt in the flesh as a man in order to exercise the authority he was given as the only begotten Son of God. To have come otherwise would have violated the precepts of God concerning the chain of authority.