Anhydrous sodium hydroxide, a common and structurally simple compound, shows spectacular isotope effects: NaOD undergoes a first-order transition, which is absent in NaOH. By combining ab initio electronic structure calculations with path integrals, we show that NaOH is an unusual example of a quantum paraelectric: zero-point quantum fluctuations stretch the weak hydrogen bonds (HBs) until they become unstable and break. By strengthening HBs via isotope substitution or applied pressure, the system can be driven down to a broken-symmetry antiferroelectric phase. We also provide a simple quantitative criterion for HB breaking in layered crystals and show that nuclear quantum effects are crucial in paraelectric to ferroelectric transitions in hydrogen-bonded hydroxides.