She was clearly chosen because she's a female superhero who actually is structured like a SUPERHERO, not a super-spy, femme fatale, assassin, or a female version of a monster character. Carol is a lead character who has starred in her own books, her powers are direct and flashy, she defies most of the tropes female characters in superhero fiction have to play by.
The reason sexists hate Carol runs a bit deeper than just the fact that she's a woman, it's that she's a woman intruding into a male role, a male space. She has the kinds of powers a male lead hero character would normally be given, and is often positioned as a leader. She doesn't use her beauty or her "nurturing" instincts or compassion, she uses her fists and her energy blasts. This makes some men deeply uncomfortable.