This world is a river, there is garbage, and there are Polypterus, and the way it's decided who's who, is by the dance they do in the movie.
Every relationship or friendship has a dynamic, one person is the water and the other the fish, for example between Togo (the older brother) and Satomi (his girlfriend) the former is the fish and the latter the water, it is said that without the water the fish cannot move, in one scene we see Satomi noticing and tying Togo's shoelaces, therefore allowing him to move freely.
Togo's coworker found a Polypterus at the same time Togo brought his brother Chihiro around, this suggests a connection between these two, Chihiro is like a Polypterus.
Traits of the Polypterus: Having a hard thing at the back of their skulls.
Being savage. We see Togo's coworker has a wound from a Polypterus bite and later Chihiro bites his own hand.
Having things their own way and being dominant. Chihiro and Naoya (his friend) discuss what their teacher's been teaching them, the teacher says "don't move, let your partner move you" and this doesn't make sense to Naoya which is understandable because if you consider the partners to be equals, which Naoya does, then neither of them would move, because they would both await their partner to move them, Chihiro however, doesn't think that way, he categorizes people as fishes and waters, and he can't decide if he's a fish or a water.
Being lonely. At one point during the movie Chihiro seems to be sympathetic, he asks Satomi if it would be better if he moved away, so she could marry Togo, it's like Chihiro realizes what kind of creature he is, he was staring at Togo and Satomi kissing on a bridge and he felt jealous but now he understands what's for the best, he knows that he's savage and selfish and can't be tamed and he doesn't want to deprive others of finding their fish/water.
There's a subtle hint at Satomi being a Polypterus, towards the beginning there's a scene where Satomi and Togo are talking about the Polypterus and they start feeling each other's skulls, Togo doesn't have a hard part and Satomi does, Togo looks at himself in the mirror with a distressed look on his face, like he's reminded what this relationship could lead to, the reason I say "reminded" is because I think he deliberately mispronounces Polypterus and refuses to acknowledge them, but later on he gives in, he then sees her tie his shoelaces which gives him reassurance, so he immediately kisses her.
Also, when she's talking to Chihiro alone, she reacts to the suggestion of him going away by saying "going with a new teacher?", very casually, like she was totally aware that there were teachers who taught people this, perhaps the dance Chihiro and Naoya do is common among everyone in this world.
However, Azusa and Chihiro's story is entirely different, Azusa notices something special about Chihiro, she takes pictures of him, breaks up with his boyfriend for him (she even bumps into Chihiro and stays in his arms when she's running from her boyfriend), and prepares herself for him by biting her hand, as if to say "I'm ready to be bitten by you and am not scared", right after Chihiro leaves home to be alone with himself for a while, his delicate dance is interrupted by Azusa who tries to force herself on him, he tells her to go back to his boyfriend and after she refuses and starts biting her own hand things spiral out of control and lead to him killing her, she could not tame the Polypterus.
The garbage in this story are people like Azusa and Naoya, people who don't know of the intricate ways of the dance and aren't marked by the hard thing at the back of their skulls.
In the end Chihiro and Naoya have one last dance that will decide their fate, Naoya loses, so he gives himself up for the Polypterus.
When the river has too much garbage in it, it floods, and when there are too many garbage people in the world I'm guessing the apocalypse happens, and that's why the movie ends with "To be continued to.... FLOODS".
Every relationship or friendship has a dynamic, one person is the water and the other the fish, for example between Togo (the older brother) and Satomi (his girlfriend) the former is the fish and the latter the water, it is said that without the water the fish cannot move, in one scene we see Satomi noticing and tying Togo's shoelaces, therefore allowing him to move freely.
Togo's coworker found a Polypterus at the same time Togo brought his brother Chihiro around, this suggests a connection between these two, Chihiro is like a Polypterus.
Traits of the Polypterus: Having a hard thing at the back of their skulls.
Being savage. We see Togo's coworker has a wound from a Polypterus bite and later Chihiro bites his own hand.
Having things their own way and being dominant. Chihiro and Naoya (his friend) discuss what their teacher's been teaching them, the teacher says "don't move, let your partner move you" and this doesn't make sense to Naoya which is understandable because if you consider the partners to be equals, which Naoya does, then neither of them would move, because they would both await their partner to move them, Chihiro however, doesn't think that way, he categorizes people as fishes and waters, and he can't decide if he's a fish or a water.
Being lonely. At one point during the movie Chihiro seems to be sympathetic, he asks Satomi if it would be better if he moved away, so she could marry Togo, it's like Chihiro realizes what kind of creature he is, he was staring at Togo and Satomi kissing on a bridge and he felt jealous but now he understands what's for the best, he knows that he's savage and selfish and can't be tamed and he doesn't want to deprive others of finding their fish/water.
There's a subtle hint at Satomi being a Polypterus, towards the beginning there's a scene where Satomi and Togo are talking about the Polypterus and they start feeling each other's skulls, Togo doesn't have a hard part and Satomi does, Togo looks at himself in the mirror with a distressed look on his face, like he's reminded what this relationship could lead to, the reason I say "reminded" is because I think he deliberately mispronounces Polypterus and refuses to acknowledge them, but later on he gives in, he then sees her tie his shoelaces which gives him reassurance, so he immediately kisses her.
Also, when she's talking to Chihiro alone, she reacts to the suggestion of him going away by saying "going with a new teacher?", very casually, like she was totally aware that there were teachers who taught people this, perhaps the dance Chihiro and Naoya do is common among everyone in this world.
However, Azusa and Chihiro's story is entirely different, Azusa notices something special about Chihiro, she takes pictures of him, breaks up with his boyfriend for him (she even bumps into Chihiro and stays in his arms when she's running from her boyfriend), and prepares herself for him by biting her hand, as if to say "I'm ready to be bitten by you and am not scared", right after Chihiro leaves home to be alone with himself for a while, his delicate dance is interrupted by Azusa who tries to force herself on him, he tells her to go back to his boyfriend and after she refuses and starts biting her own hand things spiral out of control and lead to him killing her, she could not tame the Polypterus.
The garbage in this story are people like Azusa and Naoya, people who don't know of the intricate ways of the dance and aren't marked by the hard thing at the back of their skulls.
In the end Chihiro and Naoya have one last dance that will decide their fate, Naoya loses, so he gives himself up for the Polypterus.
When the river has too much garbage in it, it floods, and when there are too many garbage people in the world I'm guessing the apocalypse happens, and that's why the movie ends with "To be continued to.... FLOODS".