Their leader would be right to do so. The sad fact is, all the "freedom of opportunity" in the world won't change the fact that our culture trains both men and women to consider women inferior. This isn't a conscious prejudice that people deliberately hold, it's an insidious mindset that is upheld by the lack of ready examples of women in positions of power or representations of competent women in the media (the fact that no woman has ever done more than "come close" to the presidency, despite being eligible to run for the office for decades, supports this). Equal opportunity laws can't change this kind of cultural imbalance; de rigeur measures can't eliminate de facto segregation, as history has repeatedly shown. De rigeur measures only allow the opportunity for individuals to eliminate de facto segregation, an opportunity that many individuals do not take.
Saying that an institution like the JLA "evolved organically" as male-dominated is to assume that men and women had equal opportunity to be represented in the first place, which simply isn't true. Technically speaking, it's just as easy to create a female superhero as a male one, but then why are there so few female superheroes, proportionally? Because recognizable positions of strength and authority are traditionally given to men, not women, and it is generally assumed that if someone is powerful and assertive that person would be male. For a woman to occupy such a position, an explanation must be given, to excuse the woman's violation of the traditional gender role. Even if we as individuals are not aware that we are demanding this, the fact is that we are.
Again, I say, Oracle is right to assume that including a male in her group might threaten her authority. Even the most well-meaning man (and I've been as guilty of this as anyone) will instinctively undercut a woman's authority, no matter what their views on gender equality happen to be. It isn't enough to say "I'm not a sexist, I believe in gender equality"; that's a good start, but to actually fight for gender equality means men being willing to take a back seat and let women have the floor, including creating spaces that are women-only and free from the influence of patriarchal values and culture, and men have got to (if you'll forgive the phrase) man up and stop complaining about being discriminated against whenever this happens, since it's always been men who have the power to discriminate in the first place. The playing field was never equal, and achieving true equality requires more than simply adjusting the status quo slightly.