Motivated by pressure experiments on café₂As₂, we propose a scenario based on local-moment physics to explain the simultaneous disappearance of magnetism, reduction of the unit cell volume, and decrease in resistivity. In this scenario, the low-pressure magnetic phase derives from Fe moments, which become screened in the paramagnetic high-pressure phase. The quantum phase transition can be described as an orbital-selective Mott transition, which is rendered first order by coupling to the lattice, in analogy to a Kondo volume collapse. Spin-fluctuation driven superconductivity competes with antiferromagnetism and may be stabilized at low temperatures in the highpressure phase. The ideas are illustrated by a suitable mean-field analysis of an Anderson lattice model.