Because it didn't?
Seriously, before you spout fireplace guesses try reading about it it.
I can show you photos of night fighter Mossies that were coated in the flaming fuel of their victims that came home, only the paint burned away. By your reasoning the wooden airplane under the paint should have gone up like kindling.
So I can just as realistically claim that the P-47D-11 should burn because it is covered in paint too.
The fact is that the Mosquito had self sealing fuel tanks and was no more prone to fires than any other aircraft.