And there we have it.
The teaching that sex is sinful.
After all, if Joseph had touched her, had sex with her, she wouldn't be pure anymore.
The notion that marital sex is impure, is rejected. But you must grasp that in Mary's case, her virginal and maternal body could not belong to two: her exclusive fidelity must be to Him Whose Son she bore.
So you might want to view her virginity in the light of her fidelity.
And the prefiguring via the Ark of the Covenant shows this so beautifully.
What is the Ark --- what is any ark? A container, a crate with handles. A box. There is nothing wrong with putting your laundry in a box, or your lunch, or your old love letters. Some of this is just a practical good ("I need something to carry our picnic lunch in") and some of it might even be, in a way, personally sacred to you ("These love letters are my most intimate and prized possession").
But you would not put these things in the Ark of the Covenant.
Why? Not because laundry and lunches and love letters are sinful, but because they are not specially consecrated in the unique way that the Ark of the Covenant and its contents are consecrated. (When I say "consecrated" I mean "Set apart to the the service of God in an exclusive manner.")
An ordinary box (ark) can be serve to carry your lunch, but not the Ark of the Covenant. The Ark of the Covenant is permanently consecrated to "sacredness" in view of the sacred things it would contain.
An ordinary woman can surely have honorable sexual union with her husband, but Mary was already permanently consecrated to "sacredness" in view of the sacred One who would come upon her and make her body fruitful, and the sacred One she would contain. Theotokos: God-carrier.
In the rich covenant theology which fills Sacred Scripture from Gen. to Rev., we can discern that Mary herself is both a person and a sign of God's Covenant faithfulness. She is like Haaretz Israel, the beloved and betrothed of God. She is like Virgin Daughter of Zion. She is the exceptional example of the faithful Jewish people. She is also the image of the Bridal and Maternal Church, Mater Ecclesia, Mother of the Redeemed (Rev 12 and Rev 22:17).
Her exclusive faithfulness to her Lord in this bridal sense is embodied in her ever-virginity. She is "set apart" for Him alone. It is her ever-fidelity.