What are the appeals and dangers of the Sorcerer's Stone? The appeal of the Philosopher's Stone, or, in America, the Sorcerer's Stone, is that it can turn regular metals into gold. More importantly, the Stone creates the Elixir of Life, which can make the user immortal. The danger is that the whole world was looking for it. A greater problem, as related later in the book, is that the user would become dependent on the Stone for the Elixir.
Why would the holder of the Stone want to give up the Stone after having it for so long? The alchemist that held the stone, Nicolas Flamel, would want to give it up after so long because he knew it could fall into the wrong hands. If Voldemort got a hold of it, he would use it to make himself immortal and continue a long reign of terror.