I have a number of reasons for putting pen to paper to describe the philosophy that guides my teaching. Firstly, writing down my thoughts and having a clear statement helps ensure my practices are, or at least aspire to be, in line with these beliefs. The largest group of stakeholders are, of course, the students themselves.
Colleagues are also an important group.
Ideally, a teaching philosophy should be openly discussed, leading to exchange of ideas and evolution of new and improved teaching practices and beliefs. I have many colleagues with considerably more teaching experience and more at ease in front of a class than myself, and some colleagues who enjoy being innovative with their teaching methods. If they are to help me in my teaching, it will help them to know something about the philosophy that guides my teaching. I would also hope that reading my philosophy might be of some worth to someone about to embark on an integrated academic career.