Question:

It is obvious that Mary had children after Jesus was born. As long as Jesus was conceived by the Holy Spirit, why was it necessary that Mary have no previous children? I am not asking why it was necessary that Jesus be conceived by the Holy Spirit—I understand that. I guess my question is, Why would it matter that Mary had other children first, as long as Jesus was conceived by the Spirit?

Answer:

I agree with you that from what is said in Scripture, it appears to be "obvious that Mary had children after Jesus was born. " Take, for example, this passage:

²When the Sabbath came, he [Jesus] began to teach in the synagogue, and many who heard him were amazed. "Where did this man get these things?" they asked. "What's this wisdom that has been given him, that he even does miracles! ³Isn't this the carpenter? Isn't this Mary's son and the brother of James, Joseph, Judas and Simon? Aren't his sisters here with us?".... (Mark 6:2-3, New International Version)

It has been argued (particularly by those who believe in the "perpetual virginity" of Mary) that the word translated "brother" (Greek "adelphos," as in "Philadelphia," "the city of brotherly love") might be taken as "cousin," but the context surely indicates that we are not talking about several households here, but one.

Incidentally, perhaps it should be noted in passing that although Jesus, James, Joseph, Judas, and Simon were all of the same household and all had Mary as their mother, Mary's husband Joseph was the physical father of James, Joseph, Judas, and Simon, but not of Jesus, who was conceived of the Holy Spirit (see Matthew 1:20; Luke 1:35). Thus, technically speaking, Jesus and his "brothers" were "half-brothers," since they only shared the same mother, but it would certainly be understandable for those in Nazareth who personally knew of the family to regard the five sons as "brothers."

Consider, also, how this passage speaks of the birth of Jesus:

²²All this took place to fulfill what the Lord had said through the prophet: ²³"The virgin will be with child and will give birth to a son, and they will call him 'Immanuel' which means, 'God with us'." ²⁴When Joseph woke up, he did what the angel of the Lord had commanded him and took Mary home as his wife. ²⁵But he had no union with her until she gave birth to a son. And he gave him the name Jesus. (Matt. 1:22-25, NIV)

The words "But he had no union with her until she gave birth to a son" certainly seem to suggest that after Mary gave birth to Jesus, Joseph did have union with her and that, having given birth to one Child, she gave birth to other children as well.

But let's get to the heart of your question: "Why was it necessary that Mary have no previous children?.... Why would it matter that Mary had other children first, as long as Jesus was conceived by the Spirit?

Here's the simple answer: It was necessary for Jesus to be born of a virgin to fulfill Isaiah's prophecy:

"Therefore the Lord himself will give you a sign: The virgin will be with child and will give birth to a son, and will call him Immanuel. (Is. 7:14, NIV)

Speaking of the birth of Christ of a virgin, Matthew (as we have already seen) says this:

²²All this took place to fulfill what the Lord had said through the prophet: ²³"The virgin will be with child and will give birth to a son, and they will call him Immanuel." (Matt. 1:22-23, NIV)

Although the exact meaning of the Hebrew word "'almah" in Isaiah 7:14 has been disputed (some—ignoring the context—take it as simply "young woman of marriageable age"), there is absolutely no dispute over the meaning of the Greek word "parthenos" in Matthew 1:23, which can have no other meaning than "virgin" (and Matthew 1:23 supplies us with an inspired interpretation of Isaiah 7:14).

Thus Scriptural prophecy found its fulfillment when our Savior was, in the familiar words of the Apostles' Creed, "conceived of the Holy Ghost, born of the virgin Mary."