I have conducted some research and found that children of observant Jewish parents often attend Jewish schools. Is this a requirement derived from halacha, or a preference on the parents' behalf?
Off the cuff, I can see 3 issues, each of which touches on a different aspect of some sort of law:
The obligation of a parent to teach a child Torah (often accomplished through the use of a teacher). This is a halacha.
The attempt to keep the child separate from outside influences. Judaism is full of laws which have, as part of their reasoning, to avoid mixing with non-Jewish elements. This discusses some parts of this idea.
Judaism views itself not as a set of discrete laws, but as a way of life which intersects with every other element. Therefore, the education system is fully integrated with Jewish law. Such awareness and religious presence cannot be effected under American law in a public school.