If catalysts can change the equilibrium of a chemical reaction, the second law of thermodynamics is false. This is a valid argument - textbooks unanimously teach it but do not explain how shifting the equilibrium would violate the second law. There is an idiotic explanation in Wikipedia that some textbooks repeat but most don't:

https://en.wikipedia.org/wiki/Catalysis
"The second law of thermodynamics describes why a catalyst does not change the chemical equilibrium of a reaction. Suppose there was such a catalyst that shifted an equilibrium. Introducing the catalyst to the system would result in a reaction to move to the new equilibrium, producing energy. Production of energy is a necessary result since reactions are spontaneous only if Gibbs free energy is produced, and if there is no energy barrier, there is no need for a catalyst. Then, removing the catalyst would also result in reaction, producing energy; i.e. the addition and its reverse process, removal, would both produce energy. Thus, a catalyst that could change the equilibrium would be a perpetual motion machine, a contradiction to the laws of thermodynamics."

Here is how the silly text above can be converted into a reasonable explanation:

Suppose there was such a catalyst that shifted an equilibrium. Introducing the catalyst to the system would result in the reaction to move to the new equilibrium and to produce some heat (we assume that this direction is the exothermic one). Part of the released heat can be converted into work. Then, removing the catalyst would restore the initial equilibrium, and in the process the reaction would absorb heat from the surroundings (this direction is the endothermic one). So introducing and removing the catalyst converts the chemical system into a heat engine that can repeatedly absorb heat from the surroundings and convert it into work, in violation of the second law of thermodynamics.

The problem for thermodynamicists (and perhaps that is the reason why clear explanations are lacking) is that catalysts OBVIOUSLY can shift the equilibrium of chemical reactions. For instance, for the dissociation-association reaction

A - B + C,

a catalyst cannot speed up both the forward and reverse reaction rates equally, due to the entirely different forward and reverse catalytic mechanisms.. In the forward (dissociation) reaction, the catalyst should just meet and split A. So the rate of the forward reaction can be substantially increased by the catalyst. In the reverse (association) reaction, the catalyst should first get together B and C. However, if the reverse reaction is diffusion-controlled (virtually any encounter between B and C produces A), the catalyst cannot accelerate it - the rate is already at its maximum.

The violation of the second law of thermodynamics by catalysts shifting the equilibrium has been proved experimentally:

https://en.wikipedia.org/wiki/Duncan%27s_Paradox
"Consider a dimeric gas (A2) that is susceptible to endothermic dissociation or exothermic recombination (A2 - 2A). The gas is housed between two surfaces (S1 and S2), whose chemical reactivities are distinct with respect to the gas. Specifically, let S1 preferentially dissociate dimer A2 and desorb monomer A, while S2 preferentially recombines monomers A and desorbs dimer A2. [...]

http://upload.wikimedia.org/wikipedi...SLTD-Fig1c.jpg

In 2014 Duncan's temperature paradox was experimentally realized, utilizing hydrogen dissociation on high-temperature transition metals (tungsten and rhenium). Ironically, these experiments support the predictions of the paradox and provide laboratory evidence for second law breakdown. These results are corroborated by other experiments that demonstrate anomalous (and differential) levels of hydrogen dissociation on heated transition metals; additional theoretical support can be found in the theory of epicatalysis. In 2015 Laboratory experiments verified examples of room temperature epicatalysis involving hydrogen-bonded diamonds on polymers. This could open the door to room temperature tests of Duncan's Paradox." [end of quotation]

Pentcho Valev