Amores Perros is a film that portrays three complex stories that are interconnected amongst each in a very subtle way. Iñárritu was interested in avoiding three short films and rather show an intertwined intelligent structure. Because if he had told the stories in chronological order the film would be lesser. So the intertwined structure is the spine of the film.
In every story we can find love, which can be pretty bitchy when it turns to vital need, and also we find hatred in the same intensity.