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Logan has aged
The movie takes place in the future. Logan grew old and his powers started to get reduced. Logan’s ability to heal became slow and he now takes a longer time to heal.
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Logan is poisoned
The Adamantium that was put in Logan’s body in the older movie is slowly poisoning him. As his ability to heal became slower, the poisoning made him weaker and weaker.
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No new mutants were born
Dr Rice managed to suppress the mutant genes in humans by introducing some food additives. This is why in the movie no mutants were born in the last 25 years and this is why Dr Rice was introduced as the man who ended the race of mutants.
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Professor X has brain damage
Professor X has a neurodegenerative disease that results in seizures if no proper medication was taken. The seizures paralyzes the people near him and could even kill them.
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Professor X killed many of the X-men
Movie fans speculate that Professor X was responsible for the Westchester incident where many mutants died. Because his brain was out of control, Logan decided to take him to a remote area in order not to kill anybody else by mistake.
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Caliban became a good guy
Caliban used to help track the mutants as seen in X-Men: Apocalypse. The DNA of those mutants was used to create more mutants. Caliban grew a conscience as he became one of the few surviving mutants and decided to help Wolverine and professor X.
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Logan has a biological daughter
The bio-weapons company Transigen used the genetic codes of dead mutants to create new generation warriors. During that process, Logan’s genetic code was used and the result was a biological daughter, Laura. (See Alien Covenant Movie Explained)
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Gabriela escaped with Laura
Gabriela, who worked in the organization Transigen that created mutant children, escaped with the mutant child Laura who is the biological daughter of Logan.
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Eden is the gathering point
Eden is not a real place, but it’s the gathering point for the mutant children. It’s the place they all agreed to meet so that they escape. Eden is real but not like it was portrayed in the book. (See The Matrix (1999) Movie Explained)
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Laura killed X-24
Laura took the Adamantium bullet Wolverine was keeping to kill himself with one day. She used it to kill X-24 by shooting him in the head.
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Logan dies because of his wounds
Logan got severely wounded. The green serum he used gave him great powers but its effect was time limited. He died under the effect of his severe wounds and his lack of ability to heal.
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The young mutants escaped
The young mutants managed to escape as the villains were killed and now the world once again has many new mutants.