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Real people do not use the word ‘gender’ with regard to any living being.
Humans do not have ‘gender,’ but they do have a sex. (and it won’t go away.
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Precisely.
Gender is a linguistic term; there are many. (C. S. Lewis wrote of the Seven Genders in his science fiction. He contrasted the masculine-feminine with the male-female to excellent effect.)
There are two - count em’ - sexes. Anything else is either an aberration or an abomination.
Sex - real sex - is by definition binary.