Chiral products from achiral reactants and 'principle of racemic mixture formation'
Because the starting material is achiral and the products are enantiomers, the reaction, by symmetry, must proceed via two enantiomeric transition states. Enantiomers have the same energy, so these two transition states have the same energy, so the rate of product formation is the same for both products. Therefore, they will be produced in equal amounts.

However, there is a complication that was not covered in your statement. There are examples of autocatalytic reactions like the Soai reaction where the product aids in catalysis and a tiny random preference for one enantiomer over the other leads to amplification of that preference. This is akin to how life uses preferentially one enantiomer instead of another, since presumably, we started with achiral materials in the primordial soup.