Talk with cats, make love with spirits

In one interview, Haruki Murakami said that the key in understanding the novel is to read it multiple times. The novel he's talking about is Kafka on the Shore, the novel that I am re-reading right now. The first time I read the novel, I thought I was really reading a fantasy novel. Talking cats, falling fishes from the sky and making love with a spirit aren't exactly my usual reading fare before. But then I continued on reading the book and along the way learned to known more about the author, his genre and slightly as well, the meaning of the novel. For the first few paragraphs, I discovered that chapters are alternated, one in the world of Kafka Tamura and the other chapter deals with things about Nakata. Still haven't found the answer why an alternating treatment of the two protaginist is needed and I bet a deeper explanation is needed, or I guess I'm just over-complicating things? That's one reason why I want to re-read the book, just what the author ordered.