A is an indefinite article. It is used to talk about a thing in general, NOT a specific thing. "A girl in white is a nurse" means that any girl dressed in white is a nurse. THE is a definite article. It is used to talk about something specific, which is already known to the listener. "THE girl in white is a nurse" means that just that particular girl dressed in white is a nurse.

Because you see her, apparently

Because it doesn't really make sense. "the" is the definite article - it refers to a particular girl. "a" is the indefinite article - it refers to no one in particular, so you can't say 'no one in particular... is a nurse". However, it is possible to say "There is a girl there in white who is a nurse". In this case, you're using the indefinite article because you don't know the girl's name but you're talking about a particular girl - the girl in white who is there (wherever there is).