Most sexist writing I encounter seems to be unintended. It used to be that masculine pronouns were used for all people, male and female. Then along came Gloria Steinem, who noticed that women constitute approximately 51% of the population. With that observation was born the construction of “he and she” and “his and her,” both quite awkward.
It’s very easy to solve this problem tactfully: make your subject plural. Instead of writing, as Henry Adams did, A teacher affects eternity; he can never tell where his influence stops, it is easy to change it to a plural subject and pronoun: To paraphrase Henry Adams, Teachers affect eternity; they can never tell where their influence stops.