RE: How do you explain psychological therianthropy?
I like a lot of what Dusty said, especially that "it's usually not a good idea to give people information they did not want." If someone asks casually, it's probably best to explain it away casually, like "I just really like/relate to these animals." If it looks like they're serious about it, you might be able to give a more serious answer.
Although I believe in both a spiritual and psychological aspect of therianthropy, I would talk about the psychological side first, since people generally agree that the brain is a real thing. Talking about souls or spirits will be a dead end if the other person thinks that souls don't exist, or animals don't have one.
So, I would first mention how humans are all animals, and we literally have an 'animal part' of our brain that acts much like the same part of other animals' brains. This is scientific fact, easy to understand; and making it 'we' relates it to the other person. Then make an extension of that premise to explain how you're different: "Some people seem to experience the animal portion of themselves more directly than others, and in a more specific way, and come to identify as a certain type of animal in some manner - known as therianthropy."
Obviously, this depends on your own beliefs and theories, but I think that starting with a concise, fairly general explanation is most palatable. Then you can give more specifics, depending on how receptive the other person is and what questions they have.