According to those holding that Jesus was literally born of a virgin, why did Paul not mention it? Matthew and Luke each open with an account of Jesus' miraculous virginal conception and birth. The virgin birth is widely seen as an essential belief in Christianity, being found for example in the Apostles' Creed.
Numerous passages in Paul's letters explicate what has been called wisdom Christology, which includes belief in a pre-existent and divine or semi-divine Christ, and he directly references Jesus' birth once. But he never mentions the virgin birth, leading some to claim that he knew of no virgin birth tradition. See for example pages 108–109 of Jesuit priest John McKenzie's book The New Testament Without Illusion:

If Matthew, chapter 1, and Luke, chapter 1, were missing from the New Testament, there would be no biblical mention of the virgin birth. ... Paul, the earliest of the New Testament writers, does not mention the virgin birth, in spite of an excellent opportunity to mention it in Galatians 4:4.
The argument from silence is generally regard as invalid when one deals with documents, unless it can be shown conclusively that the writer could not have omitted the item in question had he known it. This cannot be shown for the virgin birth. But the omission does raise speculations, as I said. The event is unusual enough for one to wonder why an author who knew of it would not mention it; and it seems that those who maintain that Mark, John and Paul knew of the virgin birth owe their readers some explanation why these authors thought it was not important enough to deserve mention.
On the other hand, those (like me) who solve the problem of the silence of all New Testament writers except Matthew and Luke by ay asserting that all the writers except these two never heard of the virgin birth also owe their readers some explanation of the supposed ignorance. This explanation I shall attempt.

How do those who hold that Jesus' mother literally gave birth to him without having had intercourse explain why Paul failed to mention it? What is an overview of their arguments?
The target audience of the writers of the gospels was to people who did not know about or did not believe in Jesus as the Messiah and Risen Lord. They included the virgin birth story because it was an important part of the narrative. Paul's target audiences, on the other hand, were already Christians and so, presumably, were already aware of the narrative of Christ. There are many other life events Paul did not mention as well.