[jessermeyer]

To confuse analogies with formal reasoning is a misuse of analogies. They are stepping stones, a kind of 'sniff test' or 'sizing up' of the mind to set the stage for more formal understanding. Is this your point?

Because, to re-use your argument, the pitfall with many formal definitions is that they are not easily understandable, whose payoff is often not much more than the analogy for the learner, but requires significantly more resources.

So, which would you prefer as an introduction? A "good enough" understanding, or no understanding because the bar of entry was too high?