Fire breathing developed as a way to help raise their young.
Being reptilian, dragons lay eggs, but eggs need warmth to mature.
Because dragons are solitary creatures, and because dragons will eat other dragons eggs at every opportunity, and male dragons will consume their own eggs if given the chance, female dragons do not have anyone to share nest sitting duties with. And since dragons spend a lot of time in cold areas like caves, mountains and such, it was really hard for them to get away to hunt during breeding season.
Like other reptiles, proto dragons had chemical glands in their mouths containing poison and other chemicals, and over time these chemicals developed combinations that would react to each other to produce heat. The proto dragon would use these chemicals to warm the rocks around the eggs so they could get away to hunt, and since they didn't have to fast during egg laying season they became bigger and stronger than other dragons.
Over time these chemicals became more and more reactive until combustion would occur when they mixed.
This is the major reason why dragons from tropical areas are smaller and don't breath fire. See komodo dragon as an example of this. They have the venom glands of their northern, cold weather cousins, but because of the climate they never needed to develop fire breathing.
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Possible duplicate of How Could Dragons Be Explained Without Magic?
– JDSweetBeat – 2015-03-10T12:58:46.183@DustinJackson I thought there was one like that, I couldn't find it! This seems to be a subset of that one, dealing only with fire-breathing. Go ahead and mark it as a dup if everyone agrees. – bowlturner – 2015-03-10T13:05:56.467
Where would fire breathing be more useful than in the cold!?! – James – 2015-03-10T13:56:03.883
I think this is a more specific question than that in the 'How could dragons be explained without magic' question. Leaving it open. – James – 2015-03-10T13:58:07.033
After comparing both questions I have come to the conclusion that you question isn't a duplicate, although the condition of 'firebreathing' implicates your question and you might find a useful answer to your question there. – JDSweetBeat – 2015-03-10T16:16:40.603
The title of this question seems really misleading to me. Mostly because someone looking for answers to this question will probably not phrase it that way. – DaaaahWhoosh – 2015-03-10T17:16:57.850
Yeah I'm not understanding this question - the title and the body don't seem to make sense taken together. – Dan Smolinske – 2015-03-10T17:35:07.653
Yes the question actually changed from when I started to when I finished, just forgot to go back and get a better one. I'll change it. – bowlturner – 2015-03-10T18:25:41.110
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...to burn Threads? (/me ducks)
– Rmano – 2015-03-11T09:54:44.317