Not always as true as you might think. There are Veblen goods [0], luxury status symbols for which the high price is part of the attraction.
More controversially, there may be Giffen goods [1]. Imagine a poor part of the world, where an average family spends half of its food budget on some cheap staple -- bread or rice or whatever -- and half on meat and fresh fruit and vegetables, but the staple part of the diet provides three-quarters of their calories. If the price of the staple rises , then their food budget will no longer provide enough calories. The only way they can make up the deficit is by buying less meat/fruit/veg and more of the staple: in other words, as the price of the staple rises, so demand for it goes up.
[0] https://en.wikipedia.org/wiki/Veblen_good [1] https://en.wikipedia.org/wiki/Giffen_good