kc kp

Equilibrium is reached when the forward and reverse reaction rates are equal. These rates are determined by the frequency of successful collisions, which is turn is determined by concentration (seen in the rate laws), temperature, activation energy, and how often molecules collide with the correct orientation (together these last three determine the rate constant, k, as shown in the Arrhenius equation).

The equilibrium constant, Kc is the ratio of the rate constants, so only variables that affect the rate constants can affect Kc. Pressure doesn't show in any of these relationships.

What is the definition of equilibrium? Forward Rate == Backward Rate (essentially).

What influences the rate of reaction? k? Concentration (e.g. rate = k[A][B]), how many collide with the correct orientation, temperature, and activation energy (see Arrhenius equation).

Kc is a ratio of [Product]/[Reacant]. You don't see pressure appear in any of these equations (rate law or Arrhenius).

Pressure may change the rate of reaction, but not the rate constant / equilibrium constant.

This can be difficult to get your head around initially. You might find it easier to look at the equations and figure it out mathematically - this helped me.