Why does put-call parity not hold, when option is American

Question

Why does put-call parity not hold, when option is American?

Answer 1

When the options are American, put–call parity does not hold, since the short position could be exercised against you, leaving you along with several exposures to the stock price. Thus we don’t know what we will be worth on expiration. Without dividends this is theoretically never optimal to exercise an American call before expiration, while an American put must be exercised when the stock falls low sufficient.