It is from the Greeks that we get the word phoenix . But others include peoples throughout Palestine, Arabia, and latter in Italy. Well, you can thank the Phoenix myth for that one. The basic story of the Phoenix is not at all set in stone, as many accounts of it survive in several Greek and Latin sources including Herodetus, Aelian, and Pliny. As recorded in these cultures, the early writing mentioning the Phoenix should be considered scientific and not mythological, meaning that none of the references to the Phoenix in ancient literature tell the actual story of the Phoenix, unless you count bestiaries.
Bestiaries record what the ancients considered fact about all the animals they knew.
This could not be considered Mythology. Though we have several authors who mention the mythical bird, it was not a very popular topic on which to write in the ancient world. Our concept of the Phoenix is due partly to Seventeenth century English poets like John Donne. While pontificating about his eternal love for a woman, he sited the Phoenix myth in allegorical comparison in his poem The Canonization. So, to one neutral thing both sexes fit.