Hard or soft copy!

The 'computrese' language is rather at contradiction with physical realities! Any writing stored in the 'computer disc', known as 'CD' is called 'Soft Copy'. For reading in paper it is usually printed out. However the printed out copy; unexplainably, is called 'Hard Copy'; while the material retained in the computer CD, is called 'Soft Copy"! Funnily enough, the 'Hard Copy', is printed in soft paper; while the original copy in the hard computer disc (CD) is called 'Soft Copy"! What a paradox in computerese vocabulary, in the words chosen to represent these copies, in two places!
In the world of 'computerese'; hard materials like the CD, is called 'soft'; while the print-out on soft paper, is called 'hard'; relating to where the copies are retained, and can later be found!
Can any knowledgeable reader, elucidate the reason or tradition that has gone in this interesting inversion of words? It will be of interest to many, with whom I have discussed the matter, with no satisfactory explanation on it! Is it a clash of 'technology' and 'language'?