At the end of their recent position paper, Arnon et al. (2025, Science) ask “[…] why language (unlike, say, birdsong) is flexible enough to be conveyed by radically different sensory systems?” We argue that language can be expressed in different modalities because its fundamentally amodal nature is enabled by a primarily left-lateralized fronto-temporal brain network that computes abstract linguistic structure independently of sensory input. Neuroimaging evidence from humans using spoken, signed, and tactile sign languages suggests that this core network is input-dependent yet modality-independent and has evolutionary precursors that already supported the multimodal communication systems of nonhuman primates. This suggests that language evolved by exapting an already flexible neural system, whereas the key underlying brain infrastructure in contemporary humans (still) operates in a flexible and amodal way.