In The Animatrix, we learn that Michael Karl Popper (likely a reference to the rationalist and philosopher), known only as The Kid in The Matrix: Revolutions, is able to escape the Matrix through sheer intellect - it's his realisation of the existence of the Matrix that alerts the Agents to him, which prompts the phone call from Neo that Michael later claims "saved" him.
This seems to be in contrast to Neo himself, who was aware that something was missing and searching for it, but still had to be led to the truth by Trinity and then Morpheus, and consume the Red Pill.
Since Neo is the One, and since there's (presumably) nothing particularly special about the Kid, why wasn't Neo able to free himself from The Matrix in the same way that the Kid did?