I perceive the phoenix as genderqueer. While firebirds are sometimes assigned a specific gender, this is not always the case. When the myths say there is but a single phoenix at any given time, it is by that definition either hermaphroditic or agendered.
Usually, the phoenix lays its egg without a partner. A phoenix needs nothing but its own will to be reborn, and no fertilization is needed to create the egg. In that sense it could be seen as asexual. In comparison, the huma of Persia is described as being one-half male and one-half female. The Chinese feng huang was in the past associated with both genders and could be seen as having both male and female natures.
Of course, now the feng huang is seen as female in complement to the Imperial dragon in symbology. Thus I tend to think of the phoenix as somewhat genderqueer - capable of male, female, both and neither as the situation calls for.
It's possible that I feel this way because I personally am genderqueer. While I can't physically shift my sex without a lot of effort, I have learned to embrace both masculine and feminine traits and mindset, and there are times when I feel like one or the other - or both, or neither - is the correct term for me. Working with firebird has helped me to see this as adaptability, a strength, rather than a weakness of not conforming to the gender markers society expects.