In Elizabethan times "rare as a black swan "did not mean that something was a rare event. It was an ironic way of saying that something was an IMPOSSIBLE event.
Elizabethans did not realise that black even swans existed.
Black swans live below the equator and the first European sighting of a black swan did not occur until 1697.
In the introduction the author states that Chastity is as rare as a black swan . This means the author believes that chastity is not seen in any woman. Avisa is repeatedly called "a rare bird "and a bird not seen". This is an allusion to the black swan. The author is ironically stating that chastity is not seen in Avisa.
This is a real indication that the full book has been written in ironia.