Because she was always locked in a dark cell because people thought she was crazy because she said she could see the future. She was always in the dark is what it said in the book.
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In her human life Mary Alice Brandon (Alice Cullen) was put in an insane asylum for 'having visions of the future'. She was said to be crazy. Being ashamed of their daughter, her parents put her in the asylum and told the public that she had died. The date for her admission into the asylum and her 'death date' are the same. Alice doesn't remember any of her human life, but has slowly obtain some knowledge of it over the years.
The reason Alice doesn't remember is because when she was bitten she was in the dark. The person who made her a vampire first found her in an asylum because of her visions.
Her name is Mary Alice Brandon, but when she became a vampire and joined Carlisle's family it was Alice Cullen. The actress who plays her in Twilight, New Moon and Eclipse is Ashley Greene
Its short for Mary Alice, which was her human name. She just goes by Alice now.
Alice has no memory of her human life because she was always in the darkness, or so she heard...