The title pretty much says it all, but I'll elaborate.
Lava is not hot enough to destroy diamond. In fact it's typically less than a third of the temperature it would take to destroy a diamond. I know the game isn't exactly steeped in realism, but there's at least a little bit of realism involved and this would be a proper change.
Most everything else could and should be destroyed by lava. Even obsidian can be melted by hotter lavas, although the lesser heated would not. Diamond on the other hand is an extremely resilient material and would not be destroyed by lava.
I find this pretty crazy. First off, you don't just single one item out. What about bedrock? Obsidian? Fire Resistance Potions? Blaze rods? Et cetera. Also, physics have nothing to do with Minecraftia. We have exploding green penises that attempt to thwart us as we delve deep into the earth and mine valuable resources, hauling up tons and tons of stone and ore when finished. Nuff said.
You ask why diamonds burn in lava?
When diamonds are the hardest material on earth?
Well, think of it like this.
You accidentally drop a piece of diamond in the lava.
It's still sitting there on the bottom, but there's nothing you can do to retrieve it.
You can't just stick your hand into three feet of molten magma.
And by the time you manage to get a fire resist potion, the diamond has already shattered into pieces. (or despawned)