A "diamond" is forever

[alatar]

First, the Silmarils had to be indestructible as a plot devise. If they were perishable, then Feanor could have destroyed them to spite everyone. Melkor could have done the same instead of bearing them in his Iron Crown. Or, when the War of Wrath was starting to go poorly for him, he could have then just smashed them. Melkor killed the trees; why not the Silmarils too?

And as stated, Feanor wasn't just thinking about Melkor, though I'm sure that stories regarding the same made him want to create something that even Melkor could not taint (as he had all of the rest of the works in Arda). Why not make something that might even confound Manwe or Aule? "Naa naa naa, I'm better than the Valar...Melkor defiled your works but not mine!" Iluvatar made certain things imperishable, and so why not Feanor? He was a little proud ya know...

And they had to resistant to Red Maw digestive systems.

And don't the jewels play some part regarding the end of the world, meaning that they would need to be (to borrow a word) null-entropic?