Why does the sun have the greatest apparent magnitude?

"Apparent magnitude" is simply how bright a celestial object is as seen from the surface of the earth. The fact that the sun is so close means that it is the brightest object in the sky. Due to the inverse square relationship of the brightness of celestial objects, our nearest star would need to be exponentially brighter to compete with the sun in this respect. SO much so that it is beyond the laws of physics as we know it for our closest star to shine this brightly.