I believe the book was written for carthartic and financial reasons, but mainly cathartic.
Kate has said that she needed to put their side of story out there. How frustrating it must have been with Amaral's book in the public domain with what he believed had happened to Madeleine. It must have been devastating and would bring a feeling of helplessness.
By writing her book, I believe it would have been good for Kate to get all her feelings out on paper, to tell her story.
Kate had kept a record of what happened right from the beginning in her diary, she wanted the details in order for Madeleine to know what happened and that they had been trying to find her from the start.
Of course Kate McCann is no writer in that sense, she obviously had help and I can imagine when asked of the way she was feeling when in the depth of knowledge that her daughter had been snatched by who knows who, all the feelings of desperation would come out. Also how everything had affected her relationship with Gerry. Everything came out as it was, she was very honest.
I believe this book was written firstly to get the truth out, secondly because it would help Kate to get it all out and thirdly it helped to fill the fund.