I have to add er to firefight. Is it firefighter or firefightter? Why

Question

I know is firefighter but I have to explain why?
Help please

Answer 1

it is "fierfighter" because that would be the correct way of spelling it, if you said "firefightter" that would make no sense because there is no reason to add an extra "t" to the word...

Answer 2

because gh is two consonants

http://www.howtospell.co.uk/doubling-up-rule