God; a mystery yet knowable
The Bible clearly states that Jesus had brothers in Matthew 12:46, and says that Joseph and Mary had relations after Jesus was born in Matthew 1:25, but the Catholic Church says that Mary was a virgin forever. How does this add up?
The fact that Mary was a virgin, both at the time of the Annunciation, and all the way until her Assumption, is the doctrine of the Perpetual Virginity of Mary.
This is one of the four Marian dogmas. The other three being the Immaculate Conception, her Divine Motherhood, and The Assumption.
The perpetual virginity of Mary is address in the Catechism of the Catholic Church;
CCC 499: The deepening of faith in the virginal motherhood led the Church to confess Mary's real and perpetual virginity even in the act of giving birth to the Son of God made man. In fact, Christ's birth "did not diminish his mother's virginal integrity but sanctified it." And so the liturgy of the Church celebrates Mary as Aeiparthenos, the "Ever-virgin".
This was a deeply held belief by the earliest Christians, and was addressed in at least three ecumenical councils; the Second Council of Constantinople (553), the Fourth Lateran Council (1215), and the Second Council of Lyons (1274).
It may surprise people to find out that some of the biggest supporters of this doctrine were the Protestant "reformers" themselves. None other than Martin Luther, Thomas Cranmer, John Wesley, and John Calvin supported the idea that Mary remained a virgin before, during, and after the birth of Christ. It wasn't until a few generations after these men that the Protestants wanted to distance, and distinguish, themselves from anything "Roman" and any kind of "Popery", that they renounced this belief.
Answering Matthew 1:25 & 12:46
I'll take a crack at the text from Mathew 1:25 first.
When Joseph woke from sleep, he did as the angel of the Lord commanded him; he took his wife, but knew her not until she had borne a son; and he called his name Jesus. Matthew 1:24-25
The thing that is pointed out in this verse is the word "until," and people use it to into that Joseph and Mary had relations, and more children, after the birth of Jesus. But this isn't what St Matthew is saying here.
St Matthew is pointing out that St Joseph had nothing to do with the conception of Jesus, and to keep Mary pure, Joseph didn't "know" her during the entire pregnancy. The word "until" isn't meant to say that after the birth they had normal marital relations, it is only saying what happened up to the time mentioned, without reference as to the events afterwards.
To get an idea of what I mean, let's look at a couple letters from St. Paul that uses the same phrase;
Till I come, attend to the public reading of Scripture, to preaching, to teaching. 1 Timothy 4:13
For he must reign until he has put all his enemies under his feet. 1 Corinthians 15:25
The first instance doesn't imply that Timothy is to preach and teach until Paul comes, but not afterward.
The second instance doesn't imply that Jesus will reign until all enemies are under His feet, and then cease to reign. We know Jesus is seated at the right hand of the Father, and will reign with Him eternally, but if we read 1Corinthians 15:25 the same way that some read Matthew 1:25 then we might conclude that Jesus wouldn't reign forever.
So we can see that "until" doesn't deal with what comes after, unless explicitly stated.
Now let's look at the other verse cited in the question, Matthew 12:46
While he was still speaking to the people, behold, his mother and his brethren stood outside, asking to speak to him. Matthew 12:46
The Church teaches, via the doctrine of Perpetual Virginity, that Mary had children other than Jesus, but the Bible mentions Jesus' brothers in several verses. So how does the Church explain this? The Church has several interpretations for "the brethren (or brothers) of Christ." I'll go over the two most common ones here.
Joseph's children
One possibility is that Joseph was an aged widower at the time of his betrothal to Mary. This would explain his their celebrate marriage after the birth of Jesus, and also his absence later in the Gospels. If Joseph was much older than Mary he would've likely been deceased by the time of Christ's passion and that's why he was absent from that pivotal moment in Jesus' life.
Jesus' cousins
The word used in this verse is adelphoi, this word is translated as "brother" in English, but doesn't necessarily mean a child of the same parents.
We have to remember that although the entire New Testament is written in Greek, Jesus was most likely speaking Aramaic. In Aramaic and in ancient Hebrew there is no word for a close male relative like the word "cousin." So when an Aramaic speaker is referring to his cousins he would call them his brothers. This is what happens in Genesis;
Abram therefore said to Lot: Let there be no quarrel, I beseech thee, between me and thee, and between my herdsmen and thy herdsmen: for we are brethren. Genesis 13:8 D-R translation
That last word in Genesis 13:8 is rendered in most English translations as "relatives" or "kinsmen" because we know that Lot isn't Abrahams brother, he is his nephew. But the word actually used in the original Hebrew is "brother." So when someone says these are Jesus' "brothers" it can just as easily mean cousin.
The Catechism sums this line of reasoning up in paragraph 500:
CCC 500: Against this doctrine the objection is sometimes raised that the Bible mentions brothers and sisters of Jesus. The Church has always understood these passages as not referring to other children of the Virgin Mary. In fact James and Joseph, "brothers of Jesus", are the sons of another Mary, a disciple of Christ, whom St. Matthew significantly calls "the other Mary". They are close relations of Jesus, according to an Old Testament expression
Spiritual "brothers"
Another possibility is that the word adelphoi is used to mean the spiritual brothers of Christ. This word is used throughout the Book of Acts to refer to all the believers. It is also used by St. Paul ten times in just his letter to the Romans, and every time it is not addressed to Paul's biological brothers, or a relative, but to his spiritual brothers in Christ.
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