Why Henry James likens fiction to a "living organism"?
Henry James was a realist. He played with point of view in his novels. He was very creative in his way of implementing literary point of view. He uses the "unreliable narrator" to show that people are not truly aware of their own self. He used interior monologue was a way to show the character's inner thoughts which added a depth to realistic fiction.
This style he used verifies his view of the world as a changing organism. In his novels the characters are always changing and growing from their interaction with other characters. This is so true to life because as human beings interact with each other, they change. Animals, as well as plants and chemicals all do the same thing.
The opposite would be a stagnant character that is a sort of caricature who remains the same throughout a novel.
I think what James is really trying to say--when he uses the analogy of a living organism-- is that when using the point-of-view the way he did, the reader could then see a whole other world within the character's mind. When the reader can see that, then we can also see how their thinking changes.
Historically speaking, after James came Virginia Wolf and James Joyce who did more of the same--playing around with point-of-view using interior monologue and showing various forms of consciousness.