Madman's Eye View
Because Taxi Driver delves so intimately into Travis Bickle's world, it feels like this film is being told in the first person. In reality, there are a few scenes that stray away from a first person perspective—we see some things and hear some things that Travis couldn't really see or hear, like when Sport and Iris are talking alone and dancing together, or when Tom and Betsy are flirtatiously chatting.
The first person perspective (or almost first person perspective) helps us really dive into Travis' mind as it goes crazier and crazier. It also forces us to empathize with him—whether we want to or not—because we see the full arc of his story. We understand that his loneliness is real and that he takes Betsy to a porn movie because he really is that clueless and socially unskilled. His isolation is inevitable and terrible.
As he goes crazier and becomes truly dangerous, we can't really hate him… even as he starts saying things like:
"The idea had been growing in my brain for some time. True force. All the king's men cannot put it back together again."
We're forced to see things the way he sees them—all the depravity and insanity of the city—which is disturbing and uncomfortable. We're not meant to agree with Travis, obviously, but we can't just dismiss him. He's the symptom of a loveless society.