Normally I wouldn’t find myself explaining sex to a therapist.

But why not.
Greg Popcak, when not supervising the St. Blog’s Institute for Nervous Patients, spends his time wondering about things. Today he wonders whether we can find any particular meaning in the fact that God became incarnate as a man rather than as a woman.
A 1999 article by Mark Brumley from The Catholic Faith confirms that the answer is yes. That meaning is to be found in the Christian understanding of human sexuality and in what Pope John Paul calls the “nuptial meaning of the human body”. God created human sexuality to represent something about Himself.
To start with: fatherhood and motherhood, while complementary, are not the same in character. They’re not quite parallel.

What is the difference between fatherhood and motherhood? A father is the “principle” or “source” of procreation in a way a mother is not. To be sure, both father and mother are parents of their offspring and in that sense both are causes of their offspring’s coming-to-be. But they are so in different ways.
Both mother and father are active agents of conception (contrary to what Aristotle thought). But the father, being male, initiates procreation; he enters and impregnates the woman, while the woman is entered and impregnated. There is an initiatory activity by the man and a receptive activity by the woman. Furthermore, modern biology tells us that the father determines the gender of the offspring (as Aristotle held, though for a different reason).
Thus, while father and mother are both parents of their offspring and both necessary for procreation, the father has a certain priority as the “source” or “principle” of procreation. (This “priority as source” is complemented by the mother’s priority as first nurturer, due to her procreating within herself and carrying the child within herself for nine months.)

This “initiatory” character of fatherhood is an earthly representation of God’s initiatory role vis-a-vis … everything else! Whether we speak of Christ and the Church, God and the soul, or God and the created world, God’s initiative comes first. We can even find this masculine-feminine polarity of God and creation in a play on words: “material” = mater.
Even within the inner life of the Holy Trinity, the Father generates on his own initiative:

Again, we draw on the analogy of human fatherhood. As we have seen, a father is the “source” of his offspring in a way a mother is not. The First Person of the Trinity is the “source” of the second Person. Thus, we call the First Person “the Father” rather than “the Mother” and the Second Person, generated by the Father yet also the Image of the Father, we call the Son.

So yes, there is something iconic about bridegrooms and brides: a cosmic dance is going on.