Why is predicting products of chemical reactions difficult?
Because you need would need to solve the Dirac equation (relativistic Schrodinger equation) for all the particles in the system to get a completely accurate result.  

Even solving the time independent non-relativistic Schrodinger equation for $\ce{H2+}$ in isolation, where there is only one electron and two protons involves approximating the protons as fixed relative to each other.  

Now imagine trying solving a system of $10^{23}$ molecules each having multiple nuclei, and dozens or even hundreds of electrons, and including time dependence!