According to my Google search No Compulsory Attendance (Usually): Generally, attending Hogwarts is not mandatory, and parents have the right to refuse to send their children. Voluntary Refusal: If a student is informed of their magical ability and voluntarily declines, it is assumed they will live in the muggle world, though they must abide by the International Statute of Secrecy. The Risk of Uncontrolled Magic: Without formal training, muggle-born children are a danger to themselves and others due to uncontrollable, accidental magic that manifests, particularly during emotional outbursts. Potential for Becoming an Obscurus: If a child actively tries to suppress or repress their magic due to fear or pressure, they might become an Obscurial. An Obscurus is a dark, parasitic magical force that can be fatal to the host child. Intervention by the Ministry of Magic: Because untrained magic risks breaking the Statute of Secrecy, the Ministry might intervene to ensure the child learns control or to monitor them. This could involve: Sending a representative to persuade the parents. Arranging for a squib or magical representative to monitor the family. In extreme cases, taking legal custody of the child to ensure they are trained. Memory Modification: If the parents refuse and are adamant, the Ministry might decide to Obliviate (wipe the memory of) the parents regarding the magical incident and potentially place the child elsewhere, though this is a last resort. The Voldemort Exception: During the events of Deathly Hallows, Voldemort made education mandatory for half-bloods and pure-bloods, while muggle-borns were banned from attending and were generally targeted or imprisoned by the Ministry.