So what does a catalyst does? Lowers the Activation energy and reduces the time taken to attain equilibrium.
By spontaneity we mean the preference of the direction of a reaction. Catalyst doesn't alter the direction of reaction. In other words, gibbs free energy change is a state function which does not depend upon the path taken by the reaction, it depends only on enthalpy and entropy(state functions) of the reaction which in turn depends upon reactants and products only .
The main use of a catalyst is to lower down the activation energy for the reaction or in other words, changing the path taken by the reaction to get completed, it cannot hinder the chemical thermodynamics. If a reaction is thermodynamically unfeasible a catalyst cannot do anything about it.