Our gender is not something purely biological, it’s something that is also reflected in our souls.
Is this Catholic teaching, and if so, how does it square with Paul saying there is no male and female in Christ?
The Catechism of the Catholic Church teaches
365 The unity of soul and body is so profound that one has to consider the soul to be the “form” of the body:[234] i.e., it is because of its spiritual soul that the body made of matter becomes a living, human body; spirit and matter, in man, are not two natures united, but rather their union forms a single nature.
369 Man and woman have been created, which is to say, willed by God: on the one hand, in perfect equality as human persons; on the other, in their respective beings
as man and woman. “Being man” or “being woman” is a reality which is good and willed by God: man and woman possess an inalienable dignity which comes to them immediately from God their Creator.[240] Man and woman are both with one and the same dignity “in the image of God”. In their “being-man” and “being-woman”, they reflect the Creator’s wisdom and goodness.
370 In no way is God in man’s image. He is neither man nor woman. God is pure spirit in which there is no place for the difference between the sexes. But the respective “perfections” of man and woman reflect something of the infinite perfection of God: those of a mother and those of a father and husband.[241]
As far as Paul saying there is no male and female in Christ, it means that it is the one and same baptism we all receive
27For all of you who were baptized into Christ have clothed yourselves with Christ. 28There is neither Jew nor Greek, slave nor free, male nor female, for you are all one in Christ Jesus. 29And if you belong to Christ, then you are Abraham’s seed and heirs according to the promise.…
Your sex, your nationality, your social status cannot exclude you from being incorporated in Christ through baptism. Baptism gives a share in the common priesthood of all believers. Through Baptism we all become sons of God and brothers to each other. However, this doesn’t mean all have the same duties, gifts and obligations.
1 Cor 12: 27 Now you are the body of Christ and individually members of it.
1 Cor 12:4 Now there are diversities of gifts, but the same Spirit.
5 And there are differences of administrations, but the same Lord.
6 And there are diversities of operations, but it is the same God which worketh all in all.
7 But the manifestation of the Spirit is given to every man to profit withal…
11 But all these worketh that one and the selfsame Spirit, dividing to every man severally as he will.