To understand what it means that the Church is the Bride of Christ, we need to understand the relation of Eve to Adam. As God made Eve from the rib taken from Adam's side while he slept, so likewise God is now making a Bride for His Son, from the blood and water that flowed from His side while He slept in death upon the cross. Eve was flesh of Adam's flesh. She was not merely the same *kind* of flesh as Adam; she was made out of Adam's very substance. Eve did not merely share the same human form or essence as Adam; their unity (even before Adam awoke) was ontological, that is, a unity of being. Her being was derived from his being, though not of his making.
When we watch an infant being born, we not only see the extraordinary sight of one human being coming out of the body of another human being, we directly experience the derivative and participatory nature of the infant's being. Eve's being was likewise derived from Adam's, though there are some important differences. She did not spring from his loins, but was taken from his side. Adam did not participate through his intellect or will in Eve's coming to be. Nor was she the result of any natural function of his organs. God alone took the rib from Adam's side, and the rib was not something already intrinsically disposed to become Eve. For these reasons, Adam was not Eve's procreator; she was co-created with him. The two additional divine acts (i.e. taking the rib from Adam, and making Eve out of the rib) formed Eve not ex nihilo but as a continuation of the divine act by which Adam had already been made.
In her coming to be, therefore, Eve participated in the very act by which Adam was given being, because her being was derived from his being. In her substance, she was Adam; she was another one of him. She was "bone of his bones, and flesh of his flesh". He had named the other animals, according to what they were. When God brought this new creature to Adam, he likewise named her according to what she was: אישה ('Ishah', woman): she who came out of Man. "She shall be called Woman, because she was taken out of Man." (Genesis 2:23)
But she was not identical to him; she was different from him in ways that complemented him. Adam was immediately drawn to her both by her likeness to him and by her difference from him -- because of the love he already had for himself. That in her that was his (i.e. which was, in some real sense, *him*) and was the same as him, he loved because he already loved himself. And that in her that was different from him, he loved because he loved the fulfillment and actualization of his own nature, and her differences from him matched him in just this complementary way. In her he found companionship that suited and completed both his human nature and his manhood. Thus when St. Paul says in Ephesians 5:28 that husbands ought to love their own wives as their own bodies, we should not read this as an arbitrary stipulation, but as a call to live according to reality, according to the ontological relation between men and women described in this account in Genesis 2.
All of this, however is a type of Christ and the Church, as St. Paul, quoting the very next verse in Genesis 2, goes on to say in Ephesians 5:31-32:
"For this cause a man shall leave his father and mother, and shall cleave to his wife; and the two shall become one flesh. This mystery is great; but I am speaking with reference to Christ and the Church."
The Church is also clearly described as the Bride of Christ in Revelation 19:7; 21:2,9. And St. Paul tells us that Christ is the second Adam. (cf. Romans 5:14; 1 Corinthians 15:22,45)
Many people affirm that the Church is the Bride of Christ, while failing to see how the Bride has to be fashioned out of that which comes from the side of Christ, such that her being and life is derived from His being and life. When God the Father brings the Church to Jesus, the second Adam will say what the first Adam said: "Bone of My bones, and flesh of My flesh", and He will give her a new name that means "taken out of Me". If we fail to recognize that the Bride must be made out of the blood and water that flowed from Christ's side, we fall into a gnosticism that treats some mental act (e.g. faith) as sufficient. Yes, God could have made Eve ex nihilo if God had wanted to do so; God is omnipotent. But if God had done so, the union of Adam and Eve would have been diminished. Their ontology would not have been shared and ordered toward each other, any more than ours is with the angels and the animals. And hence their love for one another would have been diminished. This is why merely believing in Christ is not sufficient for becoming His Bride; we must be washed in the water that flowed from His side, and eat His Body and drink His Blood. This is what it means to become a partaker of the divine nature, to become a partaker of the life of the second Adam, so that at the marriage supper of the Lamb (Revelation 19:9), He looks upon His Bride and loves her as He loves Himself, because she is His very own life, His very own flesh and blood.
How do we receive the water and blood that flowed from Christ's side? We receive them in the sacraments, especially baptism (i.e. the gateway to the other sacraments) and the Eucharist (the greatest of the sacraments). In baptism we are incorporated into the Bride. In the Eucharist we receive the living Body and Blood of the second Adam, so that we are made to live with His divine life, just as Eve was made not from inert matter taken from Adam, but from a living part of him. The life that was in Eve's body was the life that had been in Adam's body. When he looked at her, he saw his own life, his own substance, and he loved her, just as God the Father looks at His only begotten Son and sees His own Word and Thought and Being ("consubstantiálem Patri"), and loves Him. When we understand that Eve had to be made out of Adam, in order to be a bride for him, then we can better understand John 6, where Jesus says,
"The bread which I shall give for the life of the world is My flesh, ... unless you eat the flesh of the Son of Man and drink His blood, you have no life in yourselves. He who eats My flesh and drinks My blood has eternal life, and I will raise him up on the last day. For my flesh is true food, and My blood is true drink. He who eats My flesh and drinks My blood abides in Me, and I in him. As the living Father sent Me, and I live because of the Father, so he who eats Me, he also shall live because of Me." (John 6:51,53-57)
Jesus is here talking about "life", and how to acquire it. He is saying that the source of life is the "living Father", and that Jesus "lives" because of the Father, and that we can have this life only by eating the flesh of the Son of Man (i.e. the Son of Adam), and drinking His blood. This is how the Father is making a Bride for the second Adam. The second Adam has only one Bride, and we who are many, are made one Body, because we partake of one bread, which is His flesh. St. Paul says:
"Since there is one bread, we who are many are one body; for we all partake of the one bread." (1 Corinthians 10:17)
Since we receive the life of the second Adam through the sacraments, it is important, to say the least, to be able to distinguish valid sacraments from invalid sacraments. We need to be able to know whether the baptism or Eucharist we are receiving is valid, and is truly giving us the life of Christ. We do not want to be receiving mere imitations of the sacraments. If we had no way of knowing whether our sacraments are valid, we would not know whether our baptism is valid, and whether we are receiving the Body and Blood of Christ, the very Bread of Life by which "we who are many are made one Body".
The Catholic Church recognizes the validity of Protestant (Trinitarian) baptisms. But the Catholic Church (and the Orthodox) believe that Protestants do not have the Eucharist, not having maintained Apostolic succession. (This was part of the clarification that the Catholic Church released in July of last year titled Responsa ad quaestiones.) Protestants, however, believe that they do have a valid Eucharist, and that Catholics have it too.
Because Catholics and Protestants agree that sharing the Eucharist is an *essential* condition for true unity, it seems important to ask the following questions: Couldn't any heretical sect claim that its Eucharist is valid? If so, whose determination of what is necessary for a valid Eucharist is authoritative, and what does this authority teach is necessary in order to have a valid Eucharist? Claiming that this is up for "the whole Church" or "the people of God" to decide only pushes back the question or falls into circular reasoning, or appeals to something abstract like "mere Christianity".
In order to be the one Body which is the Bride of the second Adam, we need to partake of the one Bread which is His flesh and blood, taken from His side. And in order to know whether we are partaking of that one Bread, we need an authoritative witness of what is necessary for a valid Eucharist. But Scripture alone cannot play the role of authoritative witness, because it can be interpreted in many false ways, and no one holding a false interpretation thinks his own interpretation is false. Hence the issue of authority is absolutely essential, and unavoidable, for determining where is the one Bread by which we eat the flesh and blood of the second Adam and receive His life and are made into His eternal Bride.