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I have always taken it as you say “diluted” Even though it literally means a male and female of a species, it can refer to any two entities in one situation. It means that if one can be/do/have a specific thing then the other can be/do/have the same thing. I guess it is mostly about equality of rights but often it involves revenge. (eye for eye)
Also, I might be mistaken, but I don’t think this is technically an idiom. Maybe an adage.
I have never taken the gender aspect literally. To me it means that the same rules / rights / privileges apply to two different people or organizations.
If one were to apply it to a gender situation where the female is assumed to be at a significant advantage — hard to imagine there is a lot if opportunity for this — then it would be a very clever turning of the phrase, indeed.
It can work based on gender stereotype: If washing dishes is good enough for the wife- That would imply the twist that the lowly female job is the ‘advantage,’ just to be extra ironic.
Actually your point is so interesting– the structure does suggest the female gender has the advantage, or superior tastes .
I’ve also heard it put, rarely, and mostly UK, “what’s sauce for the goose is sauce for the gander.” That would fit better with the dishwashing chore.
That creates a completely different spin on “what’s GOOD for”. It doesn’t mean what is in the best interest of the goose. It’s like the Twilight Zone “To Serve Man”. It’s originally what is delicious with goose is delicious with gander.
Yuk! I am vegetarian.
Then again it’s not mystifying if one accepts that specific imagery: 2 carcasses on the table, one goose one gander, a carnivorous person contemplating sauce.
There are many adages based on specific imagery: The tortoise and the hare, the early bird catches the worm, the fox watches the hen house….