Dear Stinky Spouse,
Well, I'm afraid your husband is simply wrong.
Swirling your mouth with mouthwash may create a temporary minty feeling in your mouth, but it's not removing plaque, the bacteria that forms on our teeth.
This is going to cause him significant problems with his teeth - as well as the bad breath that you've been subjected to.
Look it up online, and show him the facts. The greater issue here, however, is that he's not listening when you tell him that something is bothering you.
But it seems that rather than telling him that this is offensive to you, you have merely asked him why he's swishing rather than brushing instead of telling him how his behavior is impacting you.
You need him to not only be healthy, but also, frankly, kissable. And that kind of bad breath sounds like a dealbreaker.
He needs to know not only the health risks to himself but how it's impacting you. A partner that cares about you is always going to take into account behaviors that their loved ones cannot tolerate.
Explain to him why this is such a risky habit, then ask him to change. If he's offended, so what?
A partnership where one person is tiptoeing around the other for fear of upsetting them is neither healthy nor sustainable. If he's hurt by your honesty, he'll get over it. And if he doesn't, if he refuses to change, it would indicate that there are bigger issues in your relationship that does not bode well for your future.
You need to muster the strength to be honest, and he needs to muster the humility to hear it, and change.