The key is the difference in binding energy of the reactants and products.
In fusion, a deuteron and triton (each with relatively low binding energy) fuse and form an alpha particle and neutron. The alpha particle is extremely stable as indicated by it's much high binding energy (see figure of binding energy curve cited by edpell).
In fission, the U or Pu nucleus fission into nuclei (and neutrons) with higher binding energy per nucleon. One possible reaction is U-236* (*=excited nucleus after neutron absorption) => Te-134 + Zr-100 + 2n. See that Zr and Te have higher binding energy per nucleon, but are less stable and decay quickly by beta decay.
It's a complicated mechanism involving nuclear (short range) and Coulomb (longer range) forces, and the nuclear structure (arrangement of nucleons in the nucleus).