Do Lists.........A fire in the making !
The usual reason for intake fires on starting is the time between the priming and turning the start switch.
I have to lay the blame firmly at the feet of instructors for the way that the majority teach the use of check lists, these lists are used as "do lists" that students slowly and deliberatly follow.
Most of these lists result in the tyro pilot taking a long time between prining the engine and turning the starter, this as a number of people above have rightly pointed out results in the priming fuel running down into the airbox risking an intake fire.
Staring the engine should be a memory drill so that the very minimum time is taken from the first prime untill the engine is stable at the recomended idle RPM and the engine T's & P's have been checked, only then should the check list be used to check that the correct checks have been done. This is why it is called a check list.
Starting a light aircraft engine is not rocket science so why do instructors try to teach it like it is?