I too think of this games as an ice breaker an way to get to know others. Not a request for someone's deepest darkest secret.
I can think of many things about me, that few people who are currently in my life know, that could be interesting to some. I also tend to tell people some things, when they start to make offensive comments, so that they know my experience is different.
An Example, my son loves to tell people his grandfather is Indian. Now my son has flaming red hair, fair skin, freckles and blue eyes. Nobody believes it, until they meet my step dad who is indeed from India and is the one grandfather my kids saw lots of growing up.
I feed feral cats at my own expense and have for three years. Very few people know about that.