The Bible uses both motherly and fatherly language and pictures to describe God and consistently resists picturing God in ways that might reduce the incomparable creator to a gendered being like the pagan gods. Yet it is often claimed that in the New Testament “Father” is used as a name for God (or at least for what later theologians think of as the first person of the Trinity). Indeed today, along with “Lord”, “Father” has become one of the most frequently used names for God among Christians. Does this naming for God imply that God is in some sense more fatherly than motherly? Is naming different from metaphorical “picture” language, such as much of the motherly God language?
In terms of the meaning of language it is not naming that is the key issue (one can claim, as Shakespeare’s Juliet does, that names are arbitrary: “What’s in a name? That which we call a rose by any other name would smell as sweet”). Perhaps the issue is rather whether this usage implies that fatherhood is an analogy for God while motherhood might be merely metaphorical language.
The distinction between metaphor and analogy was made in the Middle Ages by Thomas Aquinas and has been useful in discussion of picture language in theology. On this understanding one can present the difference between using parents as analogies, or as metaphors of God, simply. If parenting is an analogue of God then whatever parents should be, God is incomparably. While if parenting is merely a metaphor, then only some aspects of parenting are presented as being like God.
In practice, for both biblical mother language and also father language, only one aspect of parenting is in view in each context. When Jesus likens God to the loving Father in the parable (Luke 15:11-32), the point is the constant love of a father, not fatherly discipline. However, Hebrews 12:5ff. does point to fatherly discipline. There are so many examples like this that they include many, or most, aspects of fathering. Many aspects of mothering are similarly mentioned. Isaiah 66:13 refers to motherly comfort. Isaiah 42:14 points to a mother’s inability to restrain her cries in labour. Isaiah 49:14f. has the constancy of motherly love, and Matt 23:37 (and its parallel in Luke 13:34) speaks of a mother hen protecting her chicks. This range of connections suggests that both fatherhood and motherhood act as analogues of God and that neither acts merely as a metaphor.
Consider also the theological consequences if we were to say that, in Scripture, fatherhood is an analogue of God while motherhood is only a metaphor. Cultural stereotypes aside, the distinction between fathers and mothers is simple. Fathers are male and beget children. Mothers are female and bear children. If one is analogue and the other not, then this distinction must be significant for our understanding of God. God then, would not bear but beget, and would be male not female. However, such a male god, who physically fathers children, is not the God of either Old or New Testaments. Such a god is merely a Baal (the fertility god of the Canaanites).
For if God is gendered then God is a member of a class that excludes membership of a related class of beings (if God were male then God would be not-female). Such a god is partial in both senses of the term: “he” would be incomplete – for a father alone cannot produce offspring, and “he” would be biased inclined to favour or at least understand one half of humanity over the other. These limitations do not describe the biblical God. Indeed, if we examine Jesus’ own use of fatherly pictures of God, and notice how he uses “Father” as a name, we see that he minimises the gender-specific features of the picture he draws. Jesus’ father is a “motherly father”.
 Jeremias, The Prayers of Jesus, 128ff.