Oocytes are large cells that develop into an embryo upon fertilization¹. As interconnected germ cells mature into oocytes, some of them grow—typically at the expense of others that undergo cell death^2–4. We present evidence that in the nematode Caenorhabditis elegans, this cell-fate decision is mechanical and related to tissue hydraulics. An analysis of germ cell volumes and material fluxes identifies a hydraulic instability that amplifies volume differences and causes some germ cells to grow and others to shrink, a phenomenon that is related to the two-balloon instability⁵. Shrinking germ cells are extruded and they die, as we demonstrate by artificially reducing germ cell volumes via thermoviscous pumping⁶. Our work reveals a hydraulic symmetry-breaking transition central to the decision between life and death in the nematode germline.