bitcoins do not exist so they cannot be destroyed.

the blockchain which exists on every computer that runs bitcoin software, is called that because its is a chain of blocks each made up of a group of transactions...
transactions have both inputs and outputs.. by subtracting the outputs from the inputs we can determine how many "coins" each address holds but as I understand it there are no actual values or properties stored in the blockchain that represent the coins themselves. The concept of coins (just like mining) is just a way of simplifying more complex abstract ideas so that they are easier for everyday people to understand.

since there are no actual coins.. they cannot be destroyed.

of course the block-chain could be destroyed if every computer running it was compromised somehow but that would be practically impossible... hence why the idea of peer to peer decentralized crypto currency is so fascinating for everyone who uses it.