Why did Harry drop the resurrection stone?

 

So, uh Harry drops the resurrection stone so that Tom (Voldemort) who knows black magic and stuff won't get the stone and use it in his quest to be immortal.

But I think it was a bit stupid of him to just drop the stone you know what if a death eater like Bellatrix or Lucius saw it fall or what if he lived and wanted to talk to his parents?

 

And why didn't he try to destroy it like he destroyed the elder wand?