Labels like "unteachable" or "failure," once applied to a student, tend to become self-reinforcing — not because the label is accurate, but because it shapes how much effort and expectation everyone, including the student, invests going forward. A teacher who refuses to accept the label and instead insists on genuine intellectual capability, backed by real instructional effort rather than just encouraging words, can produce results that directly contradict the original label.
This isn't a claim that belief alone is sufficient — the actual instruction still has to be rigorous and well-designed. It's a claim that the ceiling on what students are asked to attempt is often set by adult expectation long before it's set by actual student capability, and that ceiling can be raised.
Marva Collins ran a school specifically for children who had already been labeled failures or unteachable by the public school system they'd come from. Rather than adjusting her expectations downward to match the label, she insisted directly to each student that they were capable of serious, rigorous intellectual work if they put in genuine effort — and backed that insistence with real instruction, having many of these previously-labeled students read and discuss challenging literature well above what their prior schools had expected of them.