This was a new word and a new idea to me, but I found helpful information in this link: https://www.gotquestions.org/narcigesis.html It explains that Narcigesis is
“the explanation of the Bible in a way that shows excessive interest
in oneself and prioritizes one’s own ideas… A person who interprets
the passage as if it were all about him is practicing narcigesis.”
“Some people with egotistical tendencies end up being narcigetes. They
view the Bible as mainly addressing their own life experiences. The
Bible is all about them: every promise is for them, and every story is
about them or their situation. Using narcigesis to interpret the story
of David and Goliath, I become David. My self-esteem demands it. (In
the story of David and Bathsheba, however, I stop being David and may
be Nathan or Uriah instead.) In the battle of Jericho, I’m Joshua
(never Achan). On the Sea of Galilee, I’m Peter walking on the water.
And so on.”
Although this might appear to be a silly approach to interpreting scripture, it is potentially very serious as a subtle way to replace Jesus with oneself. Notice how the resurrected Christ explained to the disciples that the Scriptures foretold his death and resurrection, “And beginning with Moses and the Prophets, he explained to them what was said in all the Scriptures concerning himself” (Luke 24:7 & 25-27 & 44). Narcigesis effectively tries to pull Jesus down to the same level as the person commentating (if not for the person trying to appear to be more important than Jesus – as with claims of some to actually be Jesus.) Less overt interpretations than that can creep into biblical commentaries, and so on to sites like this one.
The nearest example of this that I can think of is some instances where Jesus is claimed to be no more than a perfect, sinless man who set the example for imperfect, sinful people to follow. The claim has been made by some that as he effectively earned God’s approval by obedience, so can I. Such people will be inclined to read about what Jesus did and said with a view to then examining their own lives and to work at becoming just like Jesus – but by their own efforts and understanding.
Now, those two paragraphs above are my own opinion, so I might rightly be accused of eisegesis in a general (though not a particular) sense. Yet nobody could accuse me of narcigesis because I am disagreeing with what I would see as a narcigetic application of Scripture to oneself.
This, I hope, shows the difference between narcigesis and eisegesis, which is a matter of personal interpretation without any thought of claiming, “This passage of Scripture points to me and my experiences.” All interpretations of Scripture will invite claims of eisegesis from those who disagree with that interpretation, but that is not the same as an individual standing up and claiming the verses were fulfilled in some details of his or her own life. The narcigetic will begin by pointing to Scripture and to Christ but then focussing all attention on himself, or herself. The commentary or explanation will edge Christ into the wings while the narcigetic will take center-stage.