Within the current system of education, children are assigned to public schools of their districts unless their parents do not decide to enroll in another establishment. Qualitative education is a responsibility of parents, in the first place. Governments and officials shall never dictate parents which schools their children must attend. And parents frequently take the reins in their hands. If they decide that current establishment is useless to kids, parents feel free to transfer them to another school. Besides public schools, there are private and charter schools in every district. Low-income families may transfer kids from one public school to another if children have a conflict with staff or are bullied by peers. Besides, many parents do not restrict their search of a perfect school merely to the neighborhoods.
Apparently, children shall also have more opportunities to participate in choosing the high school where they will spend the most important years of their teenage life. It is common for students to have a priority in the selection of a college or university, but before that time parents take over all the decision making. To make things a little fairer, parents may take children with them to explore new schools and talk to the principals. Kids shall not be pushed into the establishments where teachers and peers look hostile. An unhealthy school environment may evoke inferiority complexes in kids who do not fit in the establishment chosen by their parents.
To put it short, parents have a full right to choose an appropriate school for their kids. And they shall bear responsibility for such decisions. In order to avoid any harm, parents shall cooperate with kids who will spend several years in this school and ask their opinion.