Have you ever noticed how many social pitfalls surround gum and mints? For example, if you use an item to freshen your breath and your're in mixed company, people watch and, unless they know you well, won't say anything (i.e. ask for a piece for themselves).
Etiquette generally dictates that you offer a piece to the company but there is the rub. you can't offer to share without people presuming an insult. How often do you hear, "What? Does my breath stink?" Then they cover their mouth with their hand.
Yes it does, But that's not why I'm offering. I'm trying to be polite.
On the other side, if you see someone with gum or mints you are reminded that your breath may be stale. However, asking for said item presumes the person is willing to share. Assuming you're not asking for the last piece, think about the dilemma you've created. The person with the breath freshener has a decision to make: Do they give you a piece or do they refuse and leave you to offend others with your halitosis?
On top of that, now the person with the gum or mints has to apologize for not offering to share in the first place and feels like a jerk because you didn't think ahead and bring your own piece of breath freshening goodness.
Just a random thought...