> sharing an analogy with another person is the fastest way to LOSE an argument with someone

This is true if the arguer is hostile, but as I've gotten older, if I get the sense that someone is entering an argument with the primary goal of "winning", I'll try to avoid that framing or just look for an offramp entirely.

Sure, the other party might think they "won", but they were going to think that anyway. For those more inclined to feel that the point of talking to each other is to learn from each other, I'll continue to use analogies and other things reasonable people understand.