Some of the best thermoelectrics are complex materials with rattling guests inside oversized atomic cages. Understanding the chemical and structural origins of the rattling behavior is essential to the design of thermoelectric materials. In this work, a clear connection is established between the local bonding asymmetry and anharmonic rattling modes in tetrahedrite thermoelectrics, enabled by the chemically active electron lone pairs. The studies reveal a five-atom atomic cage Sb[CuS3]Sb in Cu12Sb4S13 tetrahedrites that exhibits strong local bonding asymmetry: covalent bonding inside the CuS3 trigonal plane and weak out-of-plane bonding induced by the lone-pair electrons of Sb. This bonding asymmetry leads to out-of-plane rattling modes that are quasilocalized and anharmonic with low frequency and large amplitude, and are likely the origin of low thermal conductivity in tetrahedrites. Such knowledge highlights the importance of local structure asymmetry and lone-pair atoms in driving anharmonic rattling, providing a stepping stone to the discovery and design of next-generation thermoelectrics.