Because shorting is done by borrowing shares from someone, selling them and then buying the same number of shares at a later point to return to the party that had lent them to you initially. Since private companies by definition have their shares held by a small number of shareholders, there is no source of shares to borrow and even if an existing shareholder decided to lend them to you and you sold them to a third party, you are quite unlikely to be able to find the same number of shares on the market when the time comes to return those shares to the shareholder who lent them.