Why was the idea of the virgin birth of Jesus of Nazareth seen as important at that time? Two reasons are
1. It was seen as a fulfillment of a prophecy concerning the Messiah (Isaiah 7:14), and so was seen as evidence strengthening the claim that Jesus was the Messiah. This was important historically because the major initial audience of potential converts were people of Jewish backgrounds. So, far from disconfirming belief in Jesus as Messiah (because a virgin birth might have sounded implausible), it was supposed to be evidence in favour of a Jesus-Messiah link.
2. The idea of half-gods who were born from a god and a human woman seemed commonplace in that time and area. Many Jews were Hellenized, meaning they had adopted large parts of Greek culture. The Greeks, in turn, had many such stories (and the Romans had also adopted large parts of Greek culture, including their gods and goddesses). The idea of a virgin birth, therefore, would suggest divine origin and, therefore, that Jesus was in some important sense divine. So, again, this would tend to be seen as evidence that strengthened claims of Jesus as Messiah.
Nowadays, the situation is different. Probably, most people in secular society view the claim of a virgin birth as tending to weaken the claims in the Gospels, instead of strengthening them. Yet, what’s primary in Christianity are the things the virgin birth is supposed to support – Jesus is the Messiah, he is in some unique sense divine, that Mary was open to God’s will – and not the idea of a virgin birth itself.
Indeed, secularists do not think of themselves as theists, and so there is a prior conceptual movement, at least logically, before one gets to debating issues like whether Jesus is the Messiah.
So, if the idea of a virgin birth is acting as an obstacle to those things, then it’s doing the opposite of what it was intended to do. I.e., it was intended to be evidence in favour of those things instead of an obstacle to them. Indeed, you can believe all the important things listed above while not giving credence to the story of the virgin birth.
If this is so, why do some people hold that it’s very important to believe it? I think this largely comes from an idea often held in Christianity about the texts which have come to be known as The Bible being in some sense infallible or inerrant. The next question, then, is why people hold these texts to be inerrant (in whatever sense they hold them to be so).
Here, too, as a methodological issue it seems the idea of the inerrancy of The Bible (of whatever sort) can be an obstacle to people exploring Christianity (even if that idea is attractive to other people), because it is against the investigative spirit (as seen in what has come to be known as science – which is really just investigation). Yet, again, inerrancy-of-scripture is not required to be a Christian, and if it is acting as inimical to what is primary in Christianity, it is probably best to not worry about it!
Since the evidential situation regarding issues like the virgin birth leaves at best probabilistic arguments, where the matters are difficult to investigate, probably the best way to proceed – assuming there is something like a Christian God – is by personal revelation. So, once a relationship with God has been developed, asking for clarity on the issue. This can come later – it doesn’t need to happen at the beginning (or indeed at anytime!).
Again, for those who are seeking to build a better way, and think Christianity might have some of the answers, but find ideas like the virgin birth (or inerrancy ideas) an obstacle, don’t worry about them – set them to the side, or perhaps to be understood as useful in mythical or illustrative senses, and so on. Focus on what’s important.