I do not agree that male and female must needs find their fulfillment in each other
Me neither. I said "man and woman", not "men and women".
Please do not suppose that I'm promoting -- in the manner of Plato's Symposium -- the weird theory of Aristophanes (who wrote The Frogs, btw), of man and woman as the Zeus-severed components of a primeval Whole Human, perpetually striving to re-unite, to recover their original integrity. Man -- the sex, I mean -- does not exist without woman, nor woman without man. It seems a commonplace, scarcely worthy of comment, to say that humanity can't not exist without a coming-together of the sexes. But this is not at all the same as insisting that every single person is humanly incomplete if not paired off with a sexual complement.
Far better to say -- drawing from the same well of Eastern Christianity that I perceive in Mulieris Dignitatem -- that there's no such thing as a single "person", because personhood implies life-in-communion, knowing and being known:
"In the Book of Genesis we find another description of the creation of man - man and woman (cf. 2:18-25) - to which we shall refer shortly. At this point, however, we can say that the biblical account puts forth the truth about the personal character of the human being. Man is a person, man and woman equally so, since both were created in the image and likeness of the personal God. What makes man like God is the fact that - unlike the whole world of other living creatures, including those endowed with senses (animalia) - man is also a rational being (animal rationale)...By reflecting on the whole account found in Gen 2:18-25, and by interpreting it in light of the truth about the image and likeness of God (cf. Gen 1:26-27), we can understand even more fully what constitutes the personal character of the human being, thanks to which both man and woman are like God. For every individual is made in the image of God, insofar as he or she is a rational and free creature capable of knowing God and loving him. Moreover, we read that man cannot exist "alone" (cf. Gen 2:18); he can exist only as a "unity of the two", and therefore in relation to another human person. It is a question here of a mutual relationship: man to woman and woman to man. Being a person in the image and likeness of God thus also involves existing in a relationship, in relation to the other "I". This is a prelude to the definitive self-revelation of the Triune God: a living unity in the communion of the Father, Son and Holy Spirit."
The life-in-communion of which JPII speaks here is the very antithesis of alienated individualism, which amounts to metaphysical suicide.
... that it's when men fall in love with Christ the Bridegroom ...
JPII again: "From a linguistic viewpoint we can say that the analogy of spousal love found in the Letter to the Ephesians links what is "masculine" to what is "feminine", since, as members of the Church, men too are included in the concept of 'Bride'."
Additionally, having never actually been a woman, I don't think you have any notion...
Dear lady, I'm sure you're right. Nor do I need to, if I pray in Christ for well-loved friends and complete strangers, asking to have my prayer made pure, self-giving and cleansed of needy human self-regard. I have never been anyone except who I am. Similarly for you. Charity and humility and forgiveness derive not from gifts peculiar to one sex, nor from life experience, but because -- speaking of the crosses of this world -- we're crucified in Christ. Though every human person, man and woman, suffers privately and ineffably (the best of them striving to resist self-pity), it's Christ who gives it all the meaning it needs.
a cross on women that is a sort of shortcut to understanding.
Only when it's an occasion for grace, and that's a gift. Notwithstanding the unique case of the Mother of God, it seems a bold thing to say, that men's spiritual perfection lies in attaining "what is more natural to" the daughters of Eve, bless their hearts.
Of course, Adam was every bit as guilty.
The objective is the same -- man or woman. Women would do well to take a page from male discipline and rationality, men would do well to practice a little natural subservience and absolute trust in the notion they will cared for by whom it is they obey.
As it is, the sexes seem to be exchanging only the bad qualities natural to each.
The ultimate example being the homosexuality whereby women end up just as abusive as men (or more, given their sacramental homocide in the womb) and men end up meddlesome, calculating, shrewish and insulting whiners. Both are at the vanguard of the distorting of human being.