Well if the local school is a catholic school and you're not catholic and don't want her bought up in the catholic ethos of course she can't go there.
If the local school happened to be a boys only school she wouldn't be able to go there either.
Or if the local school you could see from your window was a private school and you didn't want to pay, or coouldn't afford to pay she couldn't go ther either.
It's not anyone's fault that the school you can see is one she can't go to, it's just the way it is. You'll have a bit further to travel every day.
I could easily walk to my local state school but choose not to send my Dd there as we want her to go the local catholic school so we drive there.
I am looking at a private school for my older 2 daughters so will have to do 2 seperate school runs. My DD1 won't be able to attend the private school, or any private scholl because she has SN's so they wouldn't accept her. Eventually she'll end up being educated in a school just for people who have SN's.
There are several types of schools
state
private
all boys
all girls
faith schools
steiner etc etc etc.
Get used to it. It's not going to change and it'll mean that sometimes our most local school isn't one that our children will be able to attend.
I can't bear the 'oh Catholic schools should let anyone in' shit. They are CATHOLIC schools, for people who want their children to bought up in the Catholic ethos. An all boys school wouldn't let in a girl just becasue it was nearer than any other school.