Because James felt there was honor & duty in serving the British Royal Navy (reinstated later by East Indian Co.). --But the only thing missing from his life was someone he "loved".
Ultimately, he loved Elizabeth and his belief system and morality is contested when Elizabeth reveals to James, that Beckett had her father killed, proving the institutions he once believed in, are now wrong (without honor).
Note: Norrington represents a dichotomy featured in the series about the order (Government-Military - Security) vs freedom (or Imperialism vs Piracy) AND themes of unrequited/disrupted love stories.
At World's End Transcript: (Note: The KISS)
Norrington [to Elizabeth]: Come with me. [she doesn’t move] Quickly!
[she nods to crew and they exit]
Elizabeth: What are you doing?
Norrington: Choosing a side. [Elizabeth exits cell. Bootstrap sees
empty cell and looks around.] Do not go to Shipwreck Cove. Beckett
knows of the meeting of the Brethren. I fear there may be a traitor
Elizabeth: It’s too late to earn my forgiveness.
Norrington: I had nothing to do with your father’s death. That doesn’t
absolve me of my other sins.
Elizabeth: Come with us. James, come with me.
Bootstrap: Who goes there?
Norrington [to Elizabeth]: Go. I will follow.
Elizabeth: You’re lying.
Norrington: Our destinies have been entwined, Elizabeth... but never
joined. [kisses her] Go! Now! [to Bootstrap] Back to your station,
Confirmed by POTC Wikipedia:
Despite having got what he wanted, Norrington came to regret his
previous actions upon learning of Beckett's hand in Governor Swann's
death, which he learned from Elizabeth after capturing the Empress. In
the end, Norrington had to make a choice and choose a side. Norrington
gave up everything, including his life, to help Elizabeth and her
crew escape from the Flying Dutchman.
Among those gathered was Elizabeth Swann, whom Norrington had first
met on the crossing from England, and had developed a friendship with
over the past eight years. However, Norrington was also in love with
Elizabeth, and, since he believed a wife was the only thing missing in
his life, wished for her hand in marriage.