Why do people believe God is genderless?
Because God is Spirit! The Spirit is bodiless! Only the Second Person of the Most Holy Trinity took on human form as man and is thus considered masculine within his human nature.
It’s important to emphasise that the point of this story isn’t to argue that God is female, but to teach us that God doesn’t fit into a neat, little box. God is beyond all categories.
This belief is stated in the Catechism of the Catholic Church when it reads that God is a mystery that is inaccessible to reason alone and that he “transcends the human distinction between the sexes. He is neither man nor woman: he is God.” (CCC 239).
239 By calling God "Father", the language of faith indicates two main things: that God is the first origin of everything and transcendent authority; and that he is at the same time goodness and loving care for all his children. God's parental tenderness can also be expressed by the image of motherhood, which emphasizes God's immanence, the intimacy between Creator and creature. the language of faith thus draws on the human experience of parents, who are in a way the first representatives of God for man. But this experience also tells us that human parents are fallible and can disfigure the face of fatherhood and motherhood. We ought therefore to recall that God transcends the human distinction between the sexes. He is neither man nor woman: he is God. He also transcends human fatherhood and motherhood, although he is their origin and standard: no one is father as God is Father.
This teaching doesn’t mean that we can’t use masculine and feminine words to describe God. Rather, gendered language can be applied to God in the form of analogy to help us understand him in a better way. Traditionally God has been viewed as a parent figure, and so mother and father references are a suitable way to describe him.
“By calling God ‘Father’, the language of Faith indicates two main things: that God is the first origin of everything and transcendent authority; and that he is at the same time goodness and loving care for all his children. God’s parental tenderness can also be expressed by the image of motherhood, which emphasises God’s immanence, the intimacy between Creator and creature. The language of faith thus draws on the human experience of parents, who are in a way the first representatives of God for man.” (CCC 239)
Throughout the Bible, masculine and feminine language is constantly used to describe God. For example, Ephesians 1:3 reads: “Blessed be the God and Father of our Lord Jesus Christ…” Yet, Isaiah 66:13 compares God to a nursing mother. “As a mother comforts her child, so I will comfort you; you shall be comforted in Jerusalem.” Leaving no opportunity for ambiguity, the Genesis account of creation most clearly shows the appropriateness of using gendered language to describe God. “Humankind was created as God’s reflection: in the divine image God created them; female and male, God made them.” (Gen. 1:27)
While some Catholics refer to God as a mother in prayer because of verses like these, there is still debate about whether it is better to describe God in wholly masculine terms. Jesus, thee best theologian of us all, for example, teaches us to pray the “Our Father”, and that baptism should be carried out “in the name of Father, and of the Son and of the Holy Spirit”.
In Christian theology, the gender of the Holy Spirit has been the subject of some debate in recent times.
The grammatical gender of the word for "spirit" is feminine in Hebrew (רוּחַ, rūaḥ), neuter in Greek (πνεῦμα, pneûma) and masculine in Latin (spiritus). The neuter Greek πνεῦμα is used in the Septuagint to translate the Hebrew רוּחַ. The pronouns used to address the Holy Spirit, however, are masculine.
The Holy Spirit was furthermore equated with the (grammatically feminine) Wisdom of God by two early Church fathers, Theophilus of Antioch (d. 180) and by Irenaeus (d. 202/3). However, the majority of theologians have, historically, identified Wisdom with Christ the Logos.
Gregory of Nazianzus in the fourth century wrote that terms like "Father" and "Son" in reference to the persons of the trinity are not to be understood as expressing essences or energies of God but are to be understood as metaphors. The same position is still held in the 1992 Catechism of the Catholic Church.
In Christian iconography, the Holy Spirit is most often represented as a dove. There is also a far less common tradition of depicting the Holy Spirit in human form, usually as male. Thus, Andrei Rublev's The Trinity represents the Trinity as the "three men" who visited Abraham at the oak of Mamre often considered a theophany of the Trinity. In at least one medieval fresco, however, in the St. Jakobus church in Urschalling, Germany, the Holy Spirit is depicted as a female. - Gender of the Holy Spirit
Early medieval church fresco of the Trinity