I just asked my Dad that question, and he had three theories, in quick succession.
1) Writing is hard because our fingers cramp up.
2) Writing is hard because we have too many words; if we wrote everything in binary, we'd only have to use 0's and 1's.
3) Writing isn't hard anymore, but we still think it is because we have the evolutionary memory of how hard it was for our ancestors who had to carve letters into stone: writing is easy, but we recoil from it out of instinct.
After we debated these responses, he settled on a more satisfactory, but less colorful answer: writing is hard because any type of writing requires careful thought in order to provide the meaning provided in conversation by intonation, hand gestures, etc. Good writing is especially hard because it requires even more careful thought, in order to be logically sound, to take other points of view into consideration, etc. Also, writing is hard because anything worth doing is hard. (My father points out that breathing is worth doing, but is not hard. So this last statement cannot in fact be taken as a universal.)