The simplistic answer is because human eyes can’t see the relatively “faint” colors of the aurora at night. Our eyes have cones and rods – the cones work during the day and the rods work at night.
"Humans use two different kinds of cells in their eyes to sense light. Cone cells, concentrated in the fovea in the central area of vision, are high resolution and detect color in bright light. These are the main cells we use for vision in the daytime. Rod cells, concentrated in the periphery around the outside of the fovea, can detect much fainter light at night, but only see in black and white and shades of gray. [Aurora] only appear to us in shades of gray because the light is too faint to be sensed by our color-detecting cone cells.” – Jerry Lodriguss
Thus the human eye views the Aurora Australis generally in “black & white.” DSLR Camera sensors don’t have this limitation. Couple that fact in with long exposure times and high ISO Settings of modern cameras means the camera sensor has a much more dynamic range of vision in the dark than we do. The same thing is true regarding the Milky Way and night photography in general.