Quasiclassical trajectory studies have been carried out for the reactions of O(P-3), F, Cl, T, and H with H-2 over a wide range of relative collision energy. For all five systems at low energy the projectile reacts only with the H atom it hits first (direct reaction), but at high energy the major product channel is the knockout reaction, where the atom hits one H atom but then goes on to react with the other one. This behavior is consistent with the direct interaction with product repulsion model and is attributed to a common feature of the potential energy surfaces, namely, a strong repulsion between the two H atoms after the system makes the rapid transition between the reactant and product regions of the surface. Evidence for the importance of knockout reactions at high energy is also seen in the angular distribution of the products, particularly in the persistence of product molecules scattered into the backward hemisphere.