But doesn't the system also oppose a change in temperature in order to keep Kc constant? Why does favouring the reverse reaction completely change Kc? Also, when heat is applied to an endothermic reaction, the reverse reaction isn't favoured so why does that increase Kc?
Good questions! When temperature is added, the concentrations of the reactants/products are completely changed which changes Kc. This is because the system will oppose the change in temperature, NOT a change in concentration. On the other hand, all other factors only change concentration directly, and will work to oppose this change in concentration. Essentially, a system with changed temperature will attempt to oppose this change in temperature, whereas a system with any other changed factor will attempt to oppose this change in
concentration. With your specific question, heating an endothermic reaction will cause a great increase in the formation of products as the forward reaction is favoured. This means Kc will become larger. Favouring the reverse reaction in the previous example I gave you would mean that the formation of reactants is greatly favoured, which means Kc will become smaller. A system opposes a change in temperature
by changing the concentrations of reactants/products, which changes Kc because Kc is
dependent on the concentration of the reactants/products.
For example, think about decreasing pressure. Decreasing pressure means there is an increase in volume, so the concentrations of all substances will decrease. The system will partially oppose this by favouring the side which produces the most particles. This does not change Kc because the system deals with the change by trying to make sure the concentrations remain in the same ratio as before. This is true for all factors excluding temperature.