Because he really liked her. He liked young girls, but especially her (you could say he was a pedophile, but that does not mean that he ever did something to her. just in the true meaning of the word: pais = kid and filia = friendship/love.)
Second, she asked him to write the story down.
Lewis Carroll had no wife as he never married. He was forbidden from marrying by the terms of his employment.
Liddell
Lewis Carroll, whose real name was Charles Lutwidge Dodgson, wrote Alice in Wonderland for Alice Liddell.
Lewis Carroll first told the story of Alice to Alice Liddell and her sisters Lorina and Edith on a boating trip they went on with Carroll's friend Robinson Duckworth.
Lewis Carroll wrote Alice in Wonderland for his friend, a little girl named Alice Liddell.
No, Carroll didn't pay Alice Liddell for Alice in Wonderland.He did however give her a hand written manuscript, especially composed and illustrated for her, which she later sold for a substantial sum.
Lewis Carroll may have thought he was in love with Alice Liddell, even though she was only a child. It is not unreasonable to say he was obsessed with her. He allegedly proposed to her when he was 31 and she was only 11.
Lewis Carroll's best friend is John Liddell.
Lewis Carroll wrote Alice's Adventures in Wonderland as a whimsical and imaginative story for a young girl named Alice Liddell, whom he enjoyed telling stories to.
Alice Liddell and Sir Basil Liddell Hart are not directly related. Alice Liddell was the inspiration for Lewis Carroll's "Alice's Adventures in Wonderland," while Sir Basil Liddell Hart was a British military strategist and historian. They share a common surname, but there is no known familial connection between them.
Lorina Liddell was the older sister of Alice Liddell, the little girl for whom Lewis Carroll wrote Alice's Adventures In Wonderland. Lorina features in the book as the Lory in Chapter 3, A Caucus-Race and a Long Tale and as Elsie in the Dormouse's story in Chapter 7, A Mad Tea-Party.
Alice's Adventures in Wonderland were not inspired by Lewis Carroll, but rather, written by him. He wrote the book for Alice Liddell, and also based it off of the new math that was gaining popularity during his time.