God Manifested the two angels as Men who went into Sodom and were guests of Lot.
Chalk one up for social norms; women wouldn't have been traveling much in those days, and these two angels were travelers. Anyway, they had to be male in order to adequately test the populace of Sodom.
Angels "Battling" the Demons, a male trait at least it is our human instincts to apply male traits to this action.
Eh, applying human emotion and traits to the bodiless powers who existed before we did seems a bit odd.
Archangel Michael appearing to Mary at the Incarnation.
It was Gabriel at the Incarnation. Ind IIRC there is no indication of gender in the text.
These and other sources give one the impression that the angels are malish is not male.
Well, there are sources that give the impression that God the Father is malish, but that doesn't actually make Him "malish" or male.
I'm not out to pick on you or anyone else, but the bodiless powers have no gender because they need no gender. Portraying someone as "gender-neutral" will always look more male-like than female-like because of the absence of certain female external characteristics. But they really aren't depicted as "male like" with a chiseled jaw, or bearded, etc.