The value that each of us places on objects or actions or services is profoundly subjective and so varies dramatically from one individual to another. For one person a pickled shark might be enormously valuable while for another it might have no value at all. Moreover there is no single unit or standard by which we can measure the degree to which any one of us values something, no valuon as we might say. This means that the only way we can work out by how much one person values something and in particular by how much they value it relative to other things is to see what else they will give up in order to get it. If someone gives up two tickets to a Madonna concert in exchange for a musical instrument that tells us they value the second item twice as highly as the first.
Money and exchanges made using money make this kind of signal of value much easier to read and also enable us to arrive at a rough aggregate or average of the relative values people place on particular things. If someone pays a thousand pounds for something, that means that at the time they spend it they value it more than the other things they could have got using the same amount of money. This means that market prices tell us how much people in the aggregate value some things as compared with others. So the price of something in a market is in a very real sense a signal of the value that it has, for people at large.
Why though do people have such a visceral reaction against this? There are many possible reasons but two in particular spring to mind. One is that it is frequently discomfiting to discover that the value we place on something is not apparently that widely shared. When people say things such as “X is valuable beyond price” what they often really mean is “I personally value X very highly but I fear that my valuation is not widely shared”. Even more significant is the constant desire to believe that you can have your cake and eat it. In the real world we are constantly having to make trade offs between things that we value and prices are the way that we discover where for most people the appropriate trade off is. Thus if we have to trade off preserving agricultural land versus building houses, the price of land in a free market would tell us how much people valued the two uses relative to each other in a specific place. Even more important, it would tell someone who wanted for example to buy land to stop it being developed what they would have to pay to do so, i.e. what else they would have to give up in order to do so.
This means that it is free exchange and choice that discovers the value of something at a given time. Many however are not prepared to accept this. They would rather use force to impose their relative valuation on others. That is the reality of pious claims to care about values rather than prices.