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.
I just experienced this in a conversation. An analogy offers an opportunity to engage with the straw man and miss the forest for the trees.
Ex:
Explainer: "Getting a spleen means cutting open the patient and taking it out. It's just like how I'm going to unzip this section of the patient-shaped doll, and remove this little purple bean. In both cases a hole is necessary in a similar location."
Hostile listener: "Nonsense! I can just buy beans at the store! So just buy a spleen! No hole!"
I’m not sure if Hofstadter puts it this way, but to me even the core aspects of your sentences in this post have roots in analogies. What does it mean to lose an argument or to spiral it to a different place? There is no place, there is no lost item, but we talk about these abstract ideas in ways that largely depend upon understanding things like physical objects and space and movement.