brogers gave you a good answer.
It's basically the same reason you sometimes use E#, B#, Cb and Fb instead of F, C, B and E natural.
You could go very indepth to explain this, and I'm gonna skip over a lot, but basically western classical music is constructed using the scales we all practice. These scales provide basic patterns for constructing, and, importantly, understanding how the music you are reading is constructed, which helps with reading speed, improvisation, memorization, all that good stuff, once you understand and have internalized these systems. This is because the patterns are the same regardless of which note you pick as your starting point - ie if you are playing C major, A flat major, C minor, G sharp minor, etc.
It'll be easier and much faster to read a D sharp major chord spelled with F double sharp than it would ever be to read the same piece with all F double sharps spelled as G naturals once you approach music from an understanding of these basic patterns.
Check out this picture and see if it gives you some kind of intuitive sense of what I'm talking about:
