According to Bulbapedia:
Cresselia's form seems to be based on a swan. Considering its crescent moon motif and the aurora-colored planetary rings around its body, it may originate from the constellation Cygnus. The rings also resemble the hagoromo gowns worn by the Tennin, spiritual beings in Japanese Buddhism, and its colour scheme of pink, yellow, and light blue, is the same as the dress worn by the Chinese goddess of the moon, Chang'e. Cresselia shares characteristics with Sarimanok, a legendary fowl with a profusely decorated head, feathered tail, and colorful wings that are said to be a symbol of good fortune. In Cresselia's Hisui Pokédex entry it states: "[Cresselia] resembles the heavenly maiden who created the Milky Way"; this "heavenly maiden" may be a reference to the Estonian goddess of birds Lindu who is said to have created the Milky Way with her tears.
Cresselia (Origin)
Tennyo
Chang'e
There are numerous references to female characters of myth, most notably Chang'e, the Tennyo, and Lindu. Each of these relates to a female lunar or spiritual being -- exactly what Cresselia is. It's reasonable to make the connection that Cresselia is female because of its inspiration being drawn from feminine sources (and it fits society's definition of "feminine").
This does not, however, inherently explain why Cresselia has a gender when most legendaries don't. It doesn't particularly matter (unless for some reason you're using Attract), as Cresselia is in the Undiscovered Egg Group and thus cannot breed. One can argue that most legendaries are genderless because they do not overtly display characteristics of either male or female -- for example, Moltres is just a bird and Cosmoem is just a literal black hole. Those that do emphasise one of the genders often do have genders -- for example, Tornadus, Thundurus and Landorus all fit the notion of being typically masculine, while Enamorus' and Latias' colour schemes are more traditionally feminine.
Again, this does not explain the numerous inconsistencies, the most glaring of which are the Tapus. If Cresselia is female, why aren't Tapu Lele or Tapu Fini? We don't currently have an answer to this, and it can be chalked up to Game Freak inconsistency (remember that they gave Heatran the ability to be either male or female, for whatever reason).
This Smogon article speculates that Cresselia is female to give the idea that "it is a living being of this world", in comparison to its counterpart Darkrai, a genderless malicious spirit.
Tl;dr Cresselia is most likely female due to its strong connection with the moon, which has historically been seen as the sun's feminine counterpart, and its female origins.
