The way I understand and use "for one," it has two interpretations, which are closely related:
because nobody else is saying anything or speaking up.... For example: A man is incessantly spanking a child in public and you and your friends stop and watch. Nobody says anything, so you say: "I, for one, think this is outrageous! I'm going to call the police."
as an example of one person (who did or didn't do something) despite what everyone else says or does... Example: "I struggled to raise my child on my own with no financial assistance from anyone. Even my own family told me to give her up for adoption so she could have a better life, but my mother, for one, never gave up on me and always knew that we would make it."