One of the neat parts of neural networks is that you have no idea what rules it's using, but it still manages to produce answers that are sometimes not entertainingly nonsensical.
I bet at a lower level, various systems in the mind fail constantly but we have enough redundant error correction to filter it out.
You might say something like "well, it has hoofs, and a mane, and a long snout, and 4 legs, etc". However, that sort of answer from a computer would probably be labeled as too generic since that could be any number of animals.
The issue is, that to you a horse is some complicated 'average' of all the examples of horses you've seen in your lifetime, that go through a complicated mechanism for you to classify it. Specifically, probabilities of different features that your eyes have extracted from seeing them.
Similarly, understanding why a neural network is doing something is very possible, however, it fails to mean much when the answer it could give is a list of, say, hundreds of vectors and weightings that contributed to its prediction.