We investigate the effect of the synthetic antiferromagnetic polarizer layer rigidness on the switching current density of spin transfer torque magnetic tunneling junction with micromagnetic simulations. In contrary to the general belief, surprisingly, the rigidness of the polarizer layer affects to the spin dynamics of the free layer and it causes the switching current density changes. When the rigidness of the synthetic antiferromagnetic polarizer layer is weakened by reducing the interlayer exchange coupling energy, we found that the switching current density can be reduced due to the more effective switching process.