Question

how did private quelch manage to anger corporal turnbull?

Answer 1

Private squelch angered corporal Turnbull by inturepting him between his lecture and publicly correcting him.

Answer 2

Corporal Turnbull was a very decorated officer, and a war veteran. On one occasion during a class session of his, wherein he is into explaining about the properties of a grenade, Private Quelch questions his knowledge and is hence dared by Corporal Turnbull to continue the class. Indeed Quelch gives a befitting lecture, but it becomes very rude to cross one's senior, especially in Army, so to teach Private Quelch a lesson, Corporal Turnbull assigns him the duties in the cookhouse.

Yes, Corporal Turnbull could have been a little less vindictive towards him, and could have treated him sympathetically.