That's derived from the idea that brushing is not about cleaning the teeth. It's about disrupting bio-films and depositing fluoride on the teeth. That's the reason why dentists recommend not rinsing your mouth after brushing. If brushing were about cleaning then clearly you would want to rinse to remove everything from your mouth. But since brushing is more about applying fluoride to your teeth, it makes more sense not to rinse as that would remove all the fluoride that you just worked to apply. (The recommendation is to brush, then take a teaspoon or two of water into your mouth to form a toothpaste slurry, swish around, then spit.)

I thus argue that flossing should come before brushing because flossing would remove the food from between your teeth, allowing fluoride to penetrate those areas.

And with regards to Listerine/mouth wash, the alcohol based stuff causes mouth cancer and hasn't shown any benefit to the reduction of cavities (I don't recall its effectiveness with respect to bad breath or gum disease). There is fluoride based mouthwash, which dentists do recommend to certain patients, but for most people there's no point since they're getting all the fluoride they need from the toothpaste. And of course there are mouth washes medicated for specific conditions, which again will be recommended by your dentist when needed.