[dsacco]

It might help if you look at a diagram such as this one to understand exactly what the code is doing: https://en.m.wikipedia.org/wiki/Feistel_cipher#/media/File%3...

So you're basically using what's known as the Luby-Rackoff construction on a provable pseudorandom function to create a pseudorandom permutation. A pseudorandom function generates output that appears random but which can repeat, which is why it cannot be invertible, and is thus unsuitable as a block cipher (you need to be able to decrypt a ciphertext to a specific plaintext).

A pseudorandom function is used as the round function in the feistel network (in the diagram, that's denoted by the F in the middle). You seed the pseudorandom function with a key K. Because the Feistel network successively transforms L and R in each round (L0, R0, L1, R1 and so on), it can be proven that even when the PRF F generates an output that has already been used, the Feistel structure will transform that output differently than the last time it was used.

In other words, the function F is not itself invertible. Invertibility is provided by the surrounding Feistel structure, because if F was already a permutation you wouldn't need anything else. F is only required to generate pseudorandom output, and the Feistel structure's additional logic is what grants invertibility to it. This is the "magic" of the Luby-Rackoff construction, which allows you to take any PRF and transform it into a PRP.