To use the tried and true analogy of human parents: yes, I allow my children to experience bad consequences, but part of my job is to make the consequences appropriate. (nakedpastor.com)
One could reasonably contend that these are not true analogies (and I think one would be right) but the net effect of these apparent analogies is to raise the question: is the dividing line between humans and animals is one of kind or of degree? (faith.org.uk)
while it is true all analogies are incomplete, your fireman analogy also has the condition of being insufficient to demonstrate your own premise. (nakedpastor.com)