Given God is genderless, why Jesus (God the Son) assumed a male form? To best of my knowledge, God has no definite gender, i.e., he's neither male nor female. Still, Jesus, God the Son, assumed a male form during his ministry. Why is that? Clearly, God the Son could have also assumed a female form, or even a genderless form. Given that, why God the Son choose to represent him as a male?
Humanity was, originally, made in the image of God. Thus was man made, in the beginning, Genesis 2:7.
Having done so, and man having been created, woman was made to be 'an help' for the man, Genesis 2:18.
This further, creative, step expresses something more of God's ultimate intention in creation.
For, ultimately, as all scripture in its progressive unfolding reveals, God's purpose is a body of persons, which, in the future, shall 'neither marry nor be given in marriage', Matthew 22:30, and shall be 'all one, in Christ Jesus', Galatians 3:28.
Thus man and woman both show forth different aspects of Deity and the ultimate purposes of Deity, in humanity. That is to say, during time, within the present creation, before that which is to come in the future, beyond time, God's purpose is expressed in the things which, presently, he made.
But he who made them is above that which he made. He who made all things is not bounded by, or constricted by, the order that he created in expression of himself. That order demonstrates things about him. It does not encapsulate he, himself.
As Jesus said, John 4:24, Pneuma ho Theos; 'Spirit, the Deity' (expressing an equivalence) or (in idiomatic English) 'God is a Spirit'.
'Gender' relates to human manifestation. It does not relate to Divine Spirit.
But God, and God's purposes, may be perceived and understood in the things which he has made, humanity - both male and female - being one very important aspect of what He made.
Jesus Christ, come in the flesh, 1 John 4:2, is a manifestation of Deity in humanity ; 'God was manifest in the flesh', 1 Timothy 3:16 [TR/KJV].
His coming does not represent the Body which was yet to be revealed ; The Church.
The Body, the Church, the Bride, is the complement of all who repent and believe the gospel and follow Jesus Christ. That whole complement of persons is seen set forth, in concept, in the creation. And, throughout scripture, femininity and womanhood demonstrate what all of God's people (as one body) shall be for Christ, the Head over all, 1 Corinthians 11:3, Ephesians 1:23, Revelation 21:9, Ephesians 5:22-32.
They - all of them, who believe - are the reality of that which is represented by created femininity.

(All references are to the TR Greek Text and to the KJV.)