The aphorism “All models are wrong, some are useful” is applicable for analogies as well. Analogies are never one to one replacement but should help to bootstrap a new concept through a known concept. Use of analogy should stop there and from there on knowledge has to be built on first principles. Why use analogies instead of first principles? Many people will have less time and effort to understand a new concept especially during business discussions, it is better to help them learn a new concept using the right analogy.
A good example is learning about resistance, current and potential difference in electricity using flow of water. Once a student gets an idea then building the knowledge should be on electrical concepts alone. It is hard to continue the analogy trying to explain electro magnetism.
I have majorly seen this problem coming up in software development where techies explain technical debt to managers and convince them to allow work to happen on that front. The debt analogy is an infamous example, managers love debts in business which helps them with a lot of working capital with less incentive to repay principal but keep paying interest. There is no interest repayment analogy in technical debt, rather it is not even a debt it is a deficiency. Deficiencies have to be addressed for growing well.
Choosing wrong analogies are much worse than using no argument at all. An example that surfaced was when we were discussing about team building and how sports teams are built; someone then took the analogy to the extreme and said programmers are like sports people and they would not be productive beyond a physical age limit. The conversation ended abruptly as the story went in a wrong direction.
As a listener we also should try to do our part to not stretch the analogies for deep understanding, instead use it as a way to quickly get onboard to a new concept.