Alchemists (correctly) observed that everything in the world was subject to disorder and decay as time progressed, but noted that gold seemed to be immune to this effect (since it is highly resistant to oxidation). Add into that the belief system that they were working with:

• That everything in the world exists on a chain of being from the most corrupt at the bottom to the most noble on top (with god being most high).

• That everything is really the same thing, and through physical processes changes its form, including up and down the chain.

And they belived that if they could figure out how to transmute a lesser metal into a more noble one then they could probably move other things up the chain of being as well. Which is why the Philospher's Stone was supposed to make people unaging and immortal, and cure all disease, in addition to transmuting lesser metals into gold. Alchemists like John of Rupescissa probably belived that creating the Stone would also bring the world closer to the divine in some way, and it was god's wish for mortals to do this.