All of Quantum Mechanics respect unitary evolution, unitary evolution can be rewinded back. Black hole evaporation breaks unitary evolution, at least in the semi-classical approximation of Hawking. If you prepare a pure quantum state it will come out as mangled thermal radiation. You cannot return to the pure quantum state from the thermal radiation (i.e. we have lost information about it).

This transition is impossible in Quantum Mechanics and it would suppose a killing blow to Quantum Mechanics if true. So a better way to rephrase our worries is that if Black Holes do not respect unitary evolution then our most precise physical theory is fundamentally wrong.