I don't think much is accomplished denying claimed miracles such as the virgin birth by saying they don't happen and aren't believable.  That is the idea of a miracle -- they don't happen and aren't believable, but, it is claimed, happened anyway -- hence there necessarily was supernatural intervention.

The only real problem I see with such claims is one of evidence.  They are extraordinary claims and therefore need extraordinary evidence before being worthy of acceptance.

There is also what may be a minor theological problem -- why should a perfect omnipotent being need to interfere with the workings of His creation?