The times today demand specialisation and there is an explosion of knowledge and information due to the internet. Experts in any field have their own clout and authority. Hence if you want to prove to your clientele that you are an expert, then you need a book, especially if you are a consultant or something like that who is hired because of your expertise.
To become a public speaker in any field
Even public speakers, who are paid to speak, need a book to point to and to establish their credentials. The only exception is if you have attained a celebrity status due to something extraordinary that you have done. If this status is strong enough, you simply can have people talk to your agent when they call. But celebrity status fades quickly and then again we come back to the book. Even former President Bill Clinton has had to write books to remain in the public eye.
Satisfying your inner need
It may be due to your ego or explanation, or you may simply want to make a record of your being in this world. However, writing a book for making a personal statement is also a good enough reason.