Question

[Sapphiox]

Why gave they'd never let a girl win a league? It's no time fair becouse it's always boys that win

 

[Grumeaux]

Because girls only do contests and Pokemon Pageant competition...............................

 

[Soaring Sid]

Cynthia and Diantha.
.
.
.
.
.
They'd have to defeat a previous champion to become champion, isn't it?

 

[Palamon]

Cynthia and Diantha.
.
.
.
.
.
They'd have to defeat a previous champion to become champion, isn't it?

Literally this.

As for on-screen girls winning a Pokemon League? Who knows? I guess the Pokemon anime doesn't care.

 

[QuietDragon]

Because girls only do contests and Pokemon Pageant competition...............................

There were girls competing even back in the first league and a Unova COTD came back in the league too, plus Bell/Bianca...

Main girls not into Contests or Performances: Misty, Iris, Mallow, Lillie...
Main girls into Contests (which involve battling, like the Grand Festivals!!!): May, Dawn. Serena's into Performances/Showcases.

We haven't seen girls win on-screen, but there's obviously women Champions easily defeating many opponents to defend their titles (for example, Cynthia, we see her battle Paul, Flint, Caitlin, etc.)...