A circular disc impacting on a water surface creates a remarkably vigorous jet. Upon impact an axisymmetric air cavity forms and eventually pinches off in a single point halfway down the cavity. Immediately after closure two fast sharp-pointed jets are observed shooting up- and downwards from the closure location, which by then has turned into a stagnation point surrounded by a locally hyperbolic flow pattern. Counter-intuitively, however, this flow is not the mechanism feeding the two jets. Using boundary-integral simulations we show that only the inertial focussing of the liquid colliding along the entire surface of the cavity provides enough energy to eject the high-speed jets. With this in mind we show how the natural description of a collapsing void (using a line of sinks along the axis of symmetry) can be continued after pinch-off to obtain a quantitative analytical model of jet formation.