The argument that the physical embodiment of the sexes is morally determinative for marriage is identical in form and substance to the argument that the physical embodiment of the races is morally determinative for slavery.
Leave aside for the moment the reference to slavery (which does appear to be akin to Godwin's law). Focus instead on the opening phrase:
The physical embodiment of the sexes.
It is a strange choice of wording. The sexes do not, cannot exist apart from "physical embodiment". There is no sexuality apart from "physical embodiment". To be human (this side of the eschaton) is to be physically male or physically female. This is not an incidental aspect to our identity as human beings. It is, rather, fundamental to such identity.
To refer to "the physical embodiment of the sexes" appears to suggest that gender is an irrelevant (if not inappropriate) category for moral theology. The reference to race and slavery, of course, emphasises this. What is striking about such a line of thought is its rejection of (and perhaps even contempt for) a catholic celebration of gender as icon rather than irrelevant accident.
The Radical Orthodoxy school has provided some important reflection on this theme. Thus Catherine Picstock on the iconic symbolism of women in the ministerial priesthood:
Allowing womens’ ordination does not remove gender from the symbolics of the Incarnation and the liturgy. On the contrary, one can think of the relation between Christ and his Bride, the Church, as echoing the relation between the Logos and the Spirit ...
In mediaeval times, it was often considered to be a Marian function with the Priest offering the Eucharistic elements as Mary bore Christ in her womb. And secondly, the Church as Bride is also the Body of Christ. This suggests that the female bride can also represent Christ as much as any male. Therefore, I want to argue for female ordination without suppressing the mystery of sexual difference.
John Milbank has also recently pointed to the significance of "the mystery of sexual difference" to understanding the place of marriage as sacrament in the Church's life and proclamation. He reminds us that rather than conforming a socially reactionary agenda, such a belief is authentically radical:
Asymmetrical reciprocity of gender needs to be reacknowledged as naturally rooted in bodily differences that, unsurprisingly, have psychic equivalents ... This conclusion is by no means simply traditional since it rejects the patriarchalism that puts men naturally on top. Instead, it newly implies that just as we need men in the home, so we need women in politics, business, the arts, academia and even the military. This prospect belongs to a radical as opposed to a liberal feminism, because it suggests that a new public role of women can truly make a difference.
A theology which embraces gay marriage and rejects "the mystery of sexual difference", Milbank goes on to warn, rejects the catholic tradition's fundamental affirmation of the created order:
This ... would mean embracing a dubious theology separating soul from body by imagining ethereal souls entirely free from their corporeal and so engendered connections. And any such development would represent a retreat from the Latin development, after Augustine, away from the excessive Platonism of some Greek Fathers (though not, perhaps, Origen) who regarded embodiment and sexual difference as a lapse from an original created perfection.
This perhaps gives an indication of what is at stake in Anglicanism's reflections on and debates over the move by various secular authorities to remove the category of gender from the definition of marriage. Irrespective of how Anglicanism makes generous, gracious pastoral provision for Christians of same-sex orientation, the iconography of gender is inherent to the Church's proclamation. To lose this iconography, this mystery, this sacramental sign, weakens the Church's ability to live out and witness to the renewal and restoration of the created order in the spousal relationship between the Bridegroom and the Bride.