Why isn't it possible to see deeper than the photosphere?

It isn't possible to see deeper than the photosphere because the sun is made up of hot gases and doesn't have a hard surface. The gases surround the Sun like a layer of fog. The gas layer becomes deeper the thicker it gets, gradually decreasing visibility to zero.

NASA scientists have determined that the photosphere is roughly 500 kilometers thick. When they estimate the size of the sun, this layer is excluded. The sunlight that reaches Earth comes from the photosphere. That's also where sunspots are formed; these are slightly cooler dark areas that can last for hours or a few months.