The first thing to recognize is that God does not have a body and therefore does not have gender in the technical sense. At the same time, God is consistently referred to as our heavenly Father in Scripture, never as a heavenly Mother.
There are a few places in Scripture where God describes Himself in motherly terms in that He does some of the things that a mother might do, like comfort or feed her children (see Hosea 11:3–4; Deuteronomy 32:18; Isaiah 42:14; 49:15; 66:13). There are about a dozen more verses where God speaks of gathering His children under His wings, as in Psalm 91:4: “He will cover you with his feathers, and under his wings you will find refuge; his faithfulness will be your shield and rampart.” Covering with feathers, it is said, is something a mother bird normally does. However, in Psalm 91 masculine pronouns are clearly used. Some cite Deuteronomy 32:11–12 as comparing God’s actions with those of a mother eagle: “Like an eagle that stirs up its nest and hovers over its young, that spreads its wings to catch them, and carries them aloft.” Notice, however, that the text does not refer to a mother eagle, and eagles are one species of bird where the father will also sit on the nest. Even if it is granted that God does some things that a mother commonly does, He is still Father—just as a human father may do some things that a mother normally does but is still the father, not the mother.
If God does not have literal gender, why does it matter if He is called Father or Mother? In brief, because God the Father is a biblical term (e.g., 1 Thessalonians 1:1), and God the Mother is not. The idea of “God as mother” usually comes to the fore when discussing issues of gender equality and gender roles as defined in the Bible. The Bible teaches that men and women have different yet complementary roles. Both men and women are made in God’s image (Genesis 1:28) and are equal before God, both in sin and salvation. However, God, for His own purposes, has designated men to be leaders in the home and church; and He holds men responsible for how they exercise their authority. Since God is the Ultimate Leader, His position is best conveyed in masculine terms such as Father and King (rather than Mother and Queen). God the Father and God the Son are both masculine titles, and the Holy Spirit is consistently referred to with masculine pronouns. God has revealed Himself as male, and He is referred to by male pronouns throughout the Bible. To call God “Mother” is unbiblical.
There are evangelical Christians who reject the idea of gender roles and male headship. They would suggest that the society in which Scripture was written was patriarchal, and, while that worldview is reflected in the Bible’s use of language, it does not carry divine endorsement. However, evangelicals who believe this would not normally go as far as to call God “Mother.” Usually, those who promote using the title God the Mother are solidly outside the evangelical camp and view the Bible as a human work, written by men and simply reinforcing the long-standing (and self-serving) patriarchal systems in which they lived.
It is reported that a well-known Bible translator was approached by someone who felt that the translation he was working on should use feminine pronouns to refer to God. The translator asked if feminine pronouns should be used to refer to the devil as well: “Resist the devil and she will flee from you.” That rejoinder was not well-received.
Unfortunately, in our society many mothers do reflect the loving, caring, and providing nature of God better than fathers who have often failed to live up to their God-given responsibilities. Many people would testify that they have trouble with the concept of God as Father because they associate Him with their absent or abusive human fathers. The solution is to get to know God the Father as He really is, not to substitute Him with God the Mother.