Let us entertain another scenario regarding matrimony. Let us pretend that woman is the matter. On its face, it seems potentially reasonable. But, I will explain how it is problematic, leaving the priest as the only one who qualifies as the singular significant physical substance/the matter. I say singular, because just as in the mass, validity is dependent on four things which are separate and separated by identifiable moments, yet it is one solemn heavenly moment. It is no different in matrimony. Therefore, once the matrimonial rite has begun, I am not going to consider the man to be his own, and the woman to be her own. It is a solemn moment. It is not an exact science.
Moving on, woman with child, is a quasi sacred character. Think of the virgin mary with Christ in her womb. That is a pretty powerful figure. God has mercy on the widow and the fatherless. This is enduring. And, it presents a powerful incentive towards honesty on the part of the man to be, you would think. However, and this is the problem, as marriage is a sacrament for the many as well(not just the Virgin Mary with St. Joseph)it would imply that consummation(and according to the modern erroneous "matter", cohabitation) comes before sanction, which is wrong. That turns that aspect of matrimony on its head. It cannot therefore possibly be. Matrimony, elevated to a sacrament by Christ at the wedding feast of Cana, cannot confuse woman with the judge. It is a temptation to hold it as such, and it is not new. I forget where I read this, but I believe there were condemned "errors" that held that a pregnant woman is an invalidating factor in matrimony. For it to be a condemned error implies that many people held this false belief.
The husband certainly doesn't satisfy the matter. The man traditionally gets down on one knee to ask the woman for her hand in marriage. She is the one who says yes. As a result of the emotion and significance of the moment, neither spouse can truly be a sober judge of consent. It only leaves us with the priest/singular and outside the church the theoretical "witness" singular.
I really have no doubt about this. Consider matter, form, and intention across the board of all of the sacraments. And, then, play that nursery song. "Which one of these is not like the other ones, which one of these doesn't belong". It is obvious that the church's current definition of matrimonial matter is "not like the other ones", and therefore "doesn't belong".
Matter is a physical substance/creature. Desire, to live together and consummate, as the modernists state, is not a creature. It is not the matter.