To me, it looks like it was chipped when it fell or was banged into the faucet, but the owner tried fixing it by rounding the point.

You could shorten it a little: mark with a sharpie the metal that needs to be removed in order to give it a normal round point (or any point you like) and then set to work with eiter a diamond file or carefully with a Dremel (prevent overheating!). I did a similar thing on a razor once and the result was very pretty.