Why is a Feistel Network able to both encrypt and decrypt just by using the round keys in a different order Using a feistel network, to encrypt something you can just use the round keys. But to decrypt it, the same order of processes is applied, however the keys are used in reverse.

My question is: What makes this property of Feistel networks possible?
In short because XOR is its own inverse operation. a XOR b XOR b is a again.

To decrypt an encrypted message we have to reverse the round function. For algorithms like AES (which is no Feistel network but a Substitution-permutation network, in short SPN) we have to reverse most operations like the MixColumn operation. This inversion is called InverseMixColumn. Theoretically we also have to do that for any Feistel network, but they nearly always use XOR as the combination of the one half with the changed other half. The inverse of XOR is again XOR, so we don't have to change it, but can just do the same again.

Take a look at a diagram of Feistel networks. Look at the output of the encryption scheme. Now try to reverse this - go back step by step. You can put one half again into the Round function, get and intermediate result and XOR this with the other half. Now you got back the input before this calculation. Repeat this until you are back at the first input which is your original plaintext. The round keys you used while doing this were the same as for the encryption, but in reversed order.