
The analogy does not depend on the premisses being true, because the 
question under discussion is not truth but arrogance. 

A similar analogy might be a medical doctor who believes that a blood 
transfusion is necessary to save the life of a child whose parents are 
Jehovah's Witnesses and so have conscientious objections to blood 
transfusion. The doctor's efforts to persuade them to agree to a blood 
transfusion could be perceived to be arrogant in precisely the same way as 
Christians could be perceived to be arrogant.

The truth or otherwise of the belief that a blood transfusion is necessary 
to save the life of the child is irrelevant here. What matters is that the 
doctor BELIEVES it to be true, and could be seen to be trying to foce his 
beliefs on the parents, and this could well be perceived as arrogance.