One never can know completely why anyone does anything. Freudian and other forms of psychological theory suggest that many of our motives are unknown even to ourselves, much less transparent to other people. From what we know of Said and his biography, we can attribute several potential motives to him, but we cannot actually know for certain what was going on inside his head during the entire process of his writing the book.
First, Said was a professor. As a professor at an elite research university, his salary and opportunities for promotion and merit pay depended to a large degree on his publishing books. Thus one obvious motive for writing a book was simply professional.
As to why he wrote about this specific topic, he describes himself as interested in the ambiguities of his own cultural position as an American citizen with an anglophone first name, an Arabic last name, and Palestinian ancestry. He states that his own experience of this sort of cultural ambiguity and blending was the source of his interest in postcolonial studies. In this work, he tries to show how the colonial experience affected not just the colonized, but also the major literary works of the colonizers.