As for hair raising, I would have reacted the same as you. It's clearly another example of just how little we know, compared to how much we think we do, in fact, know.
Given the behaviour of this 'beast', perhaps the outwardly appearance does not reflect the beauty within? You indicated that you sensed some sort of intelligence in the eyes. Any sense of malevolence etc.? From your description of its behaviour, upon contact with you, this beast was not intending any harm, maybe out foraging or travelling from someplace to somewhere? Makes me rethink the myth of the Minotaur.