I first encountered the word eisegesis in Bible study. As a Christian who believes the Bible is the Word of God, it's important to know the meaning of what the Bible says. Eisegesis is a type of interpretation that allows the reader to view the text through a lens, usually bent to his prejudices. View anything through a lens, and it's distorted, changed from the original. Exegesis is the opposite, an attempt to find the text's true original meaning.
Eisegesis is the reason you hear nonsense like the Bible endorses socialism in Acts 2, or Jesus commands His followers to be pacifists in Matthew 5. These are instances of people seeing what they want to see in the text, rather than letting the text speak for itself. Not only is the eisegetical interpretation false, it holds zero binding power since it's entirely subjective. When you realize someone's interpretation of a text is eisegetical, that should be the end of your giving it any consideration.
Mark Twain said whatever your bugaboo, you will find it therein. People have powerful prejudices. They often don't realize they're reading something that isn't there.
Take, for example, the killing of George Floyd in Minneapolis. It's taken for granted this was a racist act by the cop. This interpretation fits neatly into a perceived pattern of racism in America because the cop is white and Floyd was black. But without proof of racism these facts are incidental. What evidence is there that the cop acted the way he did because of racism? The reports are the cop knew the victim, that he had come under fire within the police department before. The text of the event doesn't directly refute the interpretation, but the interpretation doesn't logically flow from the text, either.
Critical theory is an area where eisegesis is actively encouraged. I took a semester of this in college and it was my least favorite class. We learned about different theories of critique, from feminism to queer theory to Freudian psychoanalysis to post-colonialism to structuralism to deconstructionism. There were others. We learned Edgar Allen Poe's "The Tell-Tale Heart" is actually about the narrator's homophobia and suppressed homosexual urges.
I didn't know it at the time, but that class could have done great harm. It taught me—or tried to teach me—there is no true meaning of a text per se, but a million interpretations from a million lenses I may look through. Even if I strived for objectivity, my lens would still determine what I saw. I could not rise above my upbringing, my psychology, my politics, the facts of my birth, etc. I was alone, and I had no way with words or reason to find someone to share something meaningful with.
If you accept that, really accept that the world can only be viewed through ideological and personal lenses, it will undermine your sanity and turn you into a hyper-individualized brute, more responsive to power than to reason. These days you don't need to look far to find antisocial behavior. How much is that due to the deliberate and unmitigated lensing of our shared reality into subjective experience? Quite a bit, I'd wager.