Rinsing is counter productive if you are trying to harden your teeth with fluoride mouthwash, or dealing with bacteria / sulfur deposits with antiseptic mouthwash. You're not negating it completely, but you are prematurely finishing the process that continues after you spit the rinse out. Enamel is porous, giving that fluoride some time to marinate is how it's supposed to be used. Oral bacteria are given an early reprieve from their chemical assault when you rinse...after you rinse.
Just, why? I guess I can see it if you use alcohol based crap, there is the burning issue to acknowledge I suppose.
I buy Oxyfresh mouthwash for my family. Pricier but definitely worth it. They of course say wait at least 30 before food and drink, and with the toothpaste they suggest spitting out the suds when you are done but not rinsing your mouth out with water. They must be right, because it's the only product I've ever tried where using it at night meant not having even a hint of morning mouth when I wake up.