When do people call themselves 'Master', what are they actually saying? The Mandarin for 'Master' is 'Shifu' (or Sifu). It means 'accomplished worker' or 'skilled person'. Generally, it is used as a respectful term for people in skilled manual trades - particularly where there is a relationship between apprentice and teacher. Apprentice monks can also refer to their teachers as 'Shifu'.
When asked about how to call them, most Chinese 'Grandmasters' that I have come across prefer the term - 'Laoshi', which means 'Teacher'. To me, this applies not only to humility, but also acknowledges how the terms 'Master' and 'Grandmaster' have come to signify almost mythical status.
So when a person is granted (or grants themselves) a title, what are they saying about themselves? I can't possibly answer that, because these words mean different things to other people. The titles they choose reflect their understanding of their martial art, perhaps their position within a hierarchy, the relationship they want to make with their students - many things.
To me, using the titles of 'Master' etc. elevates my position, and makes my skills seem unattainable to my students. I don't want that. I want to put the least amount of impediment between my students and their success. The term 'Teacher' - to me brings up too many bad memories of school and mandatory work. I want my title to imply success and enjoyment. I want to say that anyone can attain and exceed my level of skill. This is why I prefer the term 'coach'.