The point of the film is that she's 13 and shouldn't have to do that. The point of the film is that society forces young women to grow up and adultify themselves in various ways. Kara takes on that responsibility because she, as an adult, should be the one to handle it.
Supergirl review:
>People are gonna double back on this film in a few years
>Went in expecting absolutely nothing
>Ended up being pleasantly surprised
>A genuinely enjoyable story from start to finish
>Better than the internet is giving it credit for
>Doesn't deserve the hate it's getting