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When you look at word frequency data in English such as the Corpus Of Contemporary American English (COCA) he appears on 16th place with 6500 occurrences per mil and she at 35th place with 3210 per mil.

This is a factor of 2 in usage.

Compared to many languages, in English, he and she are only used for animate subjects, with it serving serving as the inanimate subject. And as far as I'm aware in an ambiguous or neutral context he or she or they would be used.

Therefore the null hypothesis would predict that he and she would have the same frequency, being used as pronouns by almost exactly half of the population each.

Is there something I'm missing? Or does this simply point to some deeply rooted sexism and gender imbalance?

If older works were included I could easily imagine this phenomenon being as strong as it is, because all the writers were men, but in the current language Corpus?

At the link above you can download a spreadsheet with a further subdivision of frequencies in different context and this relationship holds in most of them:

rank lemma PoS freq perMil range disp blog web TVM spok fic mag news acad blogPM webPM TVMPM spokPM ficPM magPM newsPM acadPM
16 he p 6467470 6512.91 331648 0.97 519986 638982 912036 974382 1671940 652027 871369 227209 4184.87 4968.24 7121.13 7724.88 14130.41 5171.08 7157.51 1896.72
35 she p 3188078 3210.48 206627 0.93 181410 217759 483074 354703 1283180 285458 295580 87513 1460.00 1693.13 3771.82 2812.08 10844.81 2263.90 2427.92 730.55
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    From the Merriam Webster dictionary under Definition of he (Entry 1 of 5): 2 — used in a generic sense or when the gender of the person is unspecified.
    – Robert Harvey
    Commented Mar 18, 2021 at 21:49
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    Make sure not to count He - Helium, HE - hight explosive, His Excellency, Her Excellency
    – GEdgar
    Commented Mar 18, 2021 at 21:55
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    The general use of 'he' has seen recent change to using 'they' as an unspecified singular pronoun.
    – Weather Vane
    Commented Mar 18, 2021 at 21:58
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    Yes, there is “deeply rooted sexism and gender imbalance.” Paraphrasing Karl Marx, “So far, scholars have merely interpreted the dictionary. The point, however, is to change it.” —(pronouns: he, him, his)
    – user416741
    Commented Mar 18, 2021 at 23:12
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    BTW, you can't use than with as...as equatives, even ones like twice as common as. Than can occur only with the comparative (more/less/-er) construction.
    – John Lawler
    Commented Sep 2, 2023 at 20:53

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Per Ngram, "he" was between 4 and 8 times as common as "she" up until 1970, after which this ratio rapidly declined, with the ratio now standing at roughly 1.4:1. Presumably this has something to do with the rise of second-wave feminism (see Wiki) and a reduction in sexism, but I don't think it's possible to prove this; I suspect that the increased entry of women into the workforce was the largest factor.

It used to be that "he" was sometimes used as a gender-neutral pronoun to refer to someone of unknown or unspecified gender, but the decline in that usage of "he" was itself due to its being perceived as sexist, so the ultimate cause would be the same.

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    It used to be that "he" was the only gender-neutral pronoun acceptable to teachers and many grammarians (even though they was not uncommonly used by us unrefined speakers). I believe I remember being corrected on this usage in my school years (so probably in the late 60s or early 70s). Thus, "he" would clearly have been predominant in print.
    – Peter Shor
    Commented Sep 4, 2023 at 13:18
  • There was a fad for "she" as a gender-neutral pronoun, particularly in academic use, maybe in the 1980s or 90s. But I doubt this has made much difference.
    – Stuart F
    Commented Mar 7 at 14:18

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