Mint Etiquette?

OK. I'm now reduced to worrying about such tangenital matters as:

It's polite when eating sweets to offer them to those you're with. This is an iron law, and I base most of my life around it. Except when I'm hungry. Or feeling mean. Or grumpy. Or don't like who I'm with. Or I know they're diabetic. Or etc. The recipient will no doubt get pleasure from the sweet sweet sugar. Offering chewing gum likewise. People gain pleasure from the act of chewing like some kind of ruminating animal (such as a cow or sheep, and it stops football managers from talking (cf Alex Ferguson, Sam Allardyce) or having heart attacks, so this too is something that you should offer others in your company. What I've taken to recently though, is those super-strength mints (Smint, say), which confer no benefit on the user in terms of pleasure, taste, texture, sugary sugar kick or anything of that nature. All they can possibly be used for it to make you smell less of onions. So, when I've been having one of these things, I've also been offering them round. Is this saying to the other person that I think their breath could do with smelling of mints rather than what it currently smells of? Perhaps when I'm having one too it's more of a communal thing, a shared experience, but what about when, as I have also been doing, I just whip them out of my pocket, offer them to someone, and then just put them back in my pocket, without taking one myself? Is this just the height of subtle rudeness that is likely to pique my refined and sensitive friends? Or am I being super-generous, offering round something that I'm not even going to be having myself? Or am I just trying to make people confused and paranoid?

Anyway, would you like a mint?