The crystallography of mechanically soft materials such as hybrid organic–inorganic compounds often reveals large thermal displacement factors and partially occupied lattice sites, which can arise from static or dynamic disorder. A combination of ab initio lattice dynamics and molecular dynamics simulations reveals the origin of the giant thermal displacements in the biphenyl-4,4′-dicarboxylate (BPDC) linker in the metal–organic framework UiO-67. The dihedral angle between the two phenyl rings has two equivalent minima at ±31°, which cannot be described by harmonic phonons. Instead, anharmonic switching between the minima results in the experimentally observed large thermal ellipsoids. The switching frequency is found to be similar in the topologically distinct framework IRMOF-10, suggesting that dynamic disorder is a general feature of MOFs based on BPDC and structurally similar linkers.