Put/call parity states that calls and puts at the same strike have to trade at the same volatility otherwise an arbitrage can be had. The only time this will not be the case is with either a pending dividend or if a stock is hard to borrow. Put/call parity only refers to a trade at its inception and at expiration. Many things can happen between inception and expiration in the interim that can throw this relationship out of balance. That is not a violation of put/call parity. Again, put/call parity is only used at the inception of a trade where one has the opportunity to trade its synthetic counterpart for a risk free arbitrage. If one then holds the trade all the way through to expiration, the relationship will hold. Dynamic hedging refers to one being able to maintain delta neutrality through the life of the position. Selling call spreads as a stock is dropping has nothing to do with dynamic hedging.