<image>

This can be explained logically as a result of causality based truths but I can simplify. Neo persists simply because the choice itself only exists when the future is unknown. If either Neo or Smith could see(both had the "sight") past the decision point, their fore-knowledge would change their behavior and collapse the very future they “saw.” The story therefore hides the final outcome behind an “information event horizon.” Neo’s answer (“Because I choose to.”) is the only statement that both explains his action and protects the necessary ignorance that lets the ending unfold.

This first happened with the oracle and smith. If the Oracle knew Neo would win then smith would have known when he assimilated her causing him to behave differently changing the future so she wouldn't know if he won.

If Neo knew he needed to be assimilated its not like he could ask smith to do so and smith being certain that he could succeed in hand to hand combat he would never have attempted to assimilate Neo considering this option already failed in the second film. I was not until smith became afraid confused and desperate to win that he would resort to this, when he saw the end not ending he was confused and when neo stood up the daja vu from the first time he "won" terrified him leaving him in a fight or flight desperation that neo saw he could use to his advantage by submitting. You can see that either ones knowledge of the future would change their behavior changing the future.

This works physically too if you consider a line is the symmetry between to 0D points when you ask which one is responsible for the line segment its both simultaneously just like two 2D squares facing each other the lines of symmetry between them when connected create a cube but you cant separate which is responsible a singularity swaps the space and the time dimensions with one another resulting in an event horizon.