Before answering my question, take a look at this example
$$\ce{2NOCl <=> 2NO + Cl2}$$
Let's suppose I have $\pu{2 mol/L}~\ce{NOCl},~\pu{2 mol/L}~\ce{NO}$, and $\pu{1 mol/L}~\ce{Cl2}$ in a closed system. If we were to calculate the equilibrium constant, it would be
$$K_c = \frac{(2)^2(1)}{(2)^2}$$
Now suppose I increase the concentration of both $\ce{NOCl}$ and $\ce{NO}$ by $\pu{1 mol/L}$. The equilibrium will stay the same,
$$K_c = \frac{(2+1)^2(1)}{(2+1)^2};$$
however, if I were to instead increase the concentration of both $\ce{NOCl}$ and $\ce{Cl2}$ by $\pu{1 mol/L}$, the equilibrium will shift to the product side
$$K_c = \frac{(2)^2(1+1)}{(2+1)^2}$$
Can someone explain this phenomenon in terms of rate of reaction or in terms of molecules?