Why is predicting products of chemical reactions difficult? I was going to ask whether there are software that could be used to predict the products of any given chemical reaction. However, I then noticed these two earlier questions


Chemical software for solving reactions
Software for predicting chemical reactions


where it is said such predictions are too difficult to make. What makes the prediction 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!