As this makes clear (and one of the commenters points out) the main reason people (including many feminists, I believe) donโt like the Supergirl trailer is that the hero is female.
BTW, there is just as much โbubbly nonsenseโ in male superhero shows but that gets a pass because itโs ok then.
Men wonโt like the show because itโs got a female lead and because sheโs not there to be eye candy.
Feminists will torch the show because it doesnโt hit every feminist talking point, and because itโs not dark and brooding, and because the character is realistically awkward and not some insta-badass.
A character that is sincere, thoughtful, femme, bubbly and not quite comfortable in her own skin? Yes, please. (I suspect a lot of feminists also dislike her because she is in fact very feminine. Internalized misogyny is pervasive.)
The show will last one season, I predict.