Think of the value as the cost to establish the position - for the covered call, you buy the stock (pay the spot value) sell the call (receive the premium). So, their values go in opposite directions, and they offset.
In contrast, for the protective put, you buy the stock and also buy the put (pay the premium). So the value is the sum of the two.
I am a bit late in replying, but still. Lets take an example of any good you buy. Lets say you bought a pen worth 100$ (you paid for it), so if some one asks or you want to value your pen worth what you will say. You will say worth of my pen is: 100$ (without negative sign). So, same way where we recieved we put -ve sign and where we pay we put +ve sign.
In Covered call, we buy stock and sell call. So, for buy we say +Stock and for selling we say -call. In net, S - C.
In Protective put, we buy stock and buy put. So, for buy we say +Stock and for buying put we say + Put. In net, S + P.
Finally we can say that, in case we want to see what sign we need we can just think when we will sell our position what will happen to the cash flows. When we will sell our covered call, we will receive cash flow for stock (+ve sign) and we need to pay to buy back the call (-ve cash flow).