Why does "fishwife" mean "mean woman"?

Solution 1:

The definition of a fishwife is tied to both of the definitions you listed. Wikipedia's article on the fishwife explains that:

A fishwife or fish fag is a woman who sells fish.... Fish women were notoriously loud and foul-mouthed as in the expression, To swear like a fishwife. One reason for their outspokenness is that their wares were highly perishable and so lost value if not sold quickly.

Unlike its common usage today, wife meant any woman, not just a married one. Some words still retain this meaning:

This usage stems from Old English wif (woman) and is akin to the German weib, also meaning "woman". This sense of the word is still used in Modern English in constructions such as midwife and old wives' tale.

So historically, a fishwife was just a woman who sold fish. Over time, since fishwives were often "loud and foul-mouthed," their job title became synonymous with your definition of "a bad-tempered woman with a loud voice."

Interestingly, fishwives have had different reputations in different areas. In Billingsgate, there were "the wives of Billingsgate" who:

dressed in strong 'stuff' gowns and quilted petticoats; their hair, caps and bonnets were flattened into one indistinguishable mass upon their heads. ... They smoked small pipes of tobacco, took snuff, drank gin and were known for their colourful language.

On the other hand, the fishwives of Newhaven, Scotland were:

noted for their beauty and industry, and celebrated by royalty.

Solution 2:

Handling fish is a tough, dirty job. It is not considered appropriate for a "lady." And that holds, even among the class of women who would normally be housekeepers, waitresses, etc., where public relations skills are of some importance.

As a result, fishwives, (or fisherwomen), are smellier, louder, and rougher and coarser in their manners than the other types of women described above. That translates into "meanness" in the "rude" or "low" sense of the word, including a certain amount of unpleasantness.

That doesn't necessarily make them "mean" in the bad-hearted sense of the word. Some "coarse" people I know actually have hearts of gold. But fishwives usually have exteriors that may lead people to see them (perhaps wrongly) as "mean."

Solution 3:

My mother had an illustrated book of folk tales when I was young. "The Fishmonger's Wife" was a tale not of a woman that sold fish, but a woman married to a Fishmonger, who didn't make a lot of money plying his trade. The wife's mean reputation came as she was always complaining about not having any of the finer things in life. Meanwhile, the Fishmonger was a long suffering, hard working man doing the best he could. Thus, the "fishwife" legend was begun - a woman not satisfied with a loving, hard working husband whom could not provide in the manner to which she desired, becoming resentful and haranguing to the point of........ I don't remember the ending, but I know she got her just desserts.