The opening conversation of The Matrix is special. Initially when you see it for the first time, like the entire film, you don't know what the hell is going on. It is all very artistic, intertwined and deep.

You were all wrong.

When Cypher told Trinity that "we're going to kill him" he was foreshadowing what will be explained in Matrix 4, the super matrix.

When Trinity first entered the Matrix at the age of 26, her goal was to look for "the one" and kill him, not free him. To understand this quote you need to know how exactly neo got his powers.

When the Source was created by the Architect something went wrong, there was a breech or bug in the cortex and a line of sequencing code was lost floating around the matrix until it found the right human. This piece of code ended up floating around the matrix, and eventually it found its way into a "virtual"

A quote from Matrix 4:
"It means that some people in the Super Matrix could end up as super beings, with enough power to to eventually discover what the super matrix really is. The illusion would be compromised and wed eventually lose control of the machines"

Trinity entered the Super Matrix when she was 26, her goal was to destroy this super being before he could be conciously aware that it was an illusion, and since a piece of the cortex was inside of him, the cortex would also achieve self-awareness and the super matrix would be destroyed. TRiinity couldn't kill neo because..heres another quote:

"You, Neo. You appeared, and changed my life completely, I spent all my time watching you, trying to understand you so i would be the one most prepared to go in...and destroy you"

This is just a small little spoiler...couldn't explain the whole thing otherwise i'd have ruined the the story for you all..you'll just have to be patient