Looping back to the English 1800s version, which was the top hit on my first Google for ‘Natter etymology’, I’ve found two ye old sources…
One is from Cheshire (1877), where Gnatter/Natter mean ‘to gnaw into pieces’ and Nattered means ‘exceedingly ill tempered’ (but ‘knattle’ is the much milder ‘cross’ just a few miles down the road 😂)
However, when using the ‘knatter’ spelling, it is described as synonymous to ‘knagg’ and has the example of two stepdaughters soaking their scolding, knagging stepmother in a swill tub(!) because: no ducking stool.
And the other is from Lincolnshire (1866) where ‘knattering’ meant ‘finding fault in a provoking manner’ (how we now use ‘nit picking’, perhaps?) with the example ‘he is knattering’. ‘Natter’ also uses ‘he’ but the synonym ‘worrit’ means ‘worrier’.
So, perhaps the TLDR answer to OP’s question, ‘Is this husband being sexist towards his wife?’ is…
‘Only if he’s from 1877 Cheshire and spells nattering with a silent ‘K’!