There is a scandal in the Incarnation, which is just a purification of the scandal of special revelation. Rationalists are scandalized that God would reveal His truth to a particular group of people at a particular time, let alone that He would make Himself known through one man born at a time and place inaccessible to most men. This is an objection shared in a lesser way by most Protestants who object to the idea of any man or woman being made holier by God's actions than any of us can expect to be. We have been trained to think that each Christian is or can be equal in glory to every other, a form of militant spiritual democratism. I think there is a little bit of pious leveling going on in our desire to deprive Mary (and other saints, but Mary is the major focus) of special honors.
Of course there are higher motives than simple spiritual envy. The Blessed Virgin Mother suffers from the Baby-and-Bathwater effect. Recognizing the great spiritual error and danger of elevating her in worship over her son we have been trained to bend over backwards in treating her just like any other woman, any other woman who just happened to be chosen as the vehicle for the Incarnation of the Savior of the world. That last clause should have clued us in to the insanity of such a course.
The irony here is that most of us never have a problem seeing the Holy Land as, well holy land, merely because God chose it to give to His people and especially because He walked there. We would naturally feel a special sense of spiritual presence at the spot where Christ preached, where He was arrested, and where He died, and also where He was born. These are holy places, even though these events happened 2000 years ago. Yet the idea that God's mother would also have a tangible holiness that remained upon her sends many of us Protestants into some kind of anti-Romish orbit. Such it is with Mary's perpetual virginity.
The biblical witness for Mary having other children is pretty weak. It is stated clearly that Joseph did not lie with her "until" Jesus was born. This may seem to imply that he did so afterwards but it can equally mean simply that he didn't do so through the period from their marriage to Jesus' birth without saying anything definitive about the time afterward, the point being that Mary was a virgin when Christ was conceived and born. Scripture talks about Jesus' brothers but such a term was used to identify cousins as well, there being no Greek word for "cousin" nor for "half" or "step" brother. When we supplement Scripture with the witness of the early church, Tradition, we find a unanimous witness that Mary remained a virgin, that Joseph never slept with her. Thus, the only reason for disputing her perpetual virginity is Reason, some logical or theological argument why it is either impossible or simply wrong.
One reason not to disbelieve is by refuting a bad reason to believe. There can always be bad defenses of a right doctrine or theory. If the only reason left for believing something is that most people believed it to be so, well that would still be enough. One can dismantle wrong or even idiotic explanations for something without yet being able to disprove it. I have heard a few defenses of Mary's continued virginity that I think are wrong and have been used to discredit the truth among Protestants.
1. Jesus' birth would be less miraculous if Mary had other children: I consider this pious but absurd. The miraculous nature of His birth attested to the power of God and to Jesus' divine paternity. If Mary had children naturally afterward that would do nothing to change the fact that Jesus had no early father in the flesh.
2. Mary's virginity is a necessary feature of her holiness: This is a compound error. Firstly it is erroneous in thinking that sex after marriage is less pure than virginity. This idea makes holy marriage, an institution God created before the Fall, into a compromise with Sin. I know that sometimes marriage is looked at this way both inside and outside the church (outside the compromise is seen as good and natural as opposed to unnatural and irrational, think Billy Joel's "Only the Good Die Young"), but this is neither correct biblically nor theologically, nor is it actually official church teaching, especially with regard to married women. Secondly it makes Mary into a divine figure who possesses attributes necessary to her divinity. God would hardly be seen as God if He were not omnipotent or holy or good or a few other things we associate with being God. So Mary here is seen as needing to have certain qualities that make he what she is. Her virginity is not just something which she possessed at one time but something which she must possess. It becomes like a special heroic power. "Lo, she shall smite the enemy with the power of her virginity!"
Was Mary holy because she was a virgin. No. She was holy because she was chosen to be Jesus' mother. Certainly her being a virgin was a factor in her being chosen, but that was a matter of timing. She was holy due to her maternity, not her virginity. Thus she would have remained holy as Jesus' mater, virgin or not.
3. It would be a sin for Joseph to have sex with her afterward: This is closer to the mark, but still, I believe false. That is, I do not think that Joseph would have sinned if he had taken her as his wife physically as well as legally, unless he thought it was a sin.
This gets us to what I consider to be the convincing reason for believing Mary to have remained a virgin: I can easily see Joseph, rightly or wrongly, believing that it would be wrong for him to enter the place from which God's Son had emerged. If he was a pious Jew it seems entirely logical that learning that God had used his virgin wife to be the vessel of God's Son would bring to mind images of the ark of the Covenant and of the fate of those who touched it unworthily. Would it have seemed right for him to use for his own fleshly desires the vessel of the Lord? It seems incredible to me now to imagine that these questions would not have been in his mind. Would I have reacted the same way thinking as a 21st century Protestant if I was married to the mother of God? I can't say, but I think it foolish to imagine that my priorities would not be radically transformed by such an event.
The upshot of all this is that while I don't believe it was necessary morally or theologically for Mary to remain a virgin I can't see any logical reason why Joseph would act in any way to change her condition. And as there is no clear witness that she ever had any other children by a human father it seems irrational to insist that she did.