Points Closer to Zero on the Mandelbrot Set

Question

Can someone explain to me why there are points outside the Mandelbrot set which are closer to zero than a point radially outward which is in the set? I know this is true, but my intuition tells me that because complex multiplication adds the angles from the real axis and multiplies the magnitudes, numbers a number with the same angle but a smaller magnitude than one in the set should also be included.