Since lead and other metals are not composed of fire, air, earth, and water, it's not possible to adjust the percentages of those elements and turn them into gold. Though alchemy never succeeded, that didn't stop people from claiming to have solved the ancient riddle.

Why is alchemy no longer accepted?

Why is alchemy no longer accepted? Because it was based on mystical belief instead of the scientific method (which had not been codified for most of alchemy's existance). It is completely wrong, even if it stumbled on techniques which are still useful.

Is alchemy actually possible?

Short answer: Depending on how you define alchemy, yes, it's possible, and we do it. Long answer: Alchemists were basically the precursors to chemists, in the same way that philosophers conjecturing about the four elements were the precursor to physics.