Rather than saying that men want sex more than women, one might say that men want more sex than women. Reversing those two words substantially changes the meaning, if you know what I mean. The first refers to intensity and the second refers to frequency.
You have accurately discerned that sexual desire, sexual appetite, or sex drive, however one might phrase it, occurs in individual members of the human population over a range of intensity. The range might be represented as a normal, or “bell” curve such as this one:
The right end of the curve would represent people with an unusually low sexual appetite and the left end would represent those whose appetite is unusually high, while the middle would represent a normal or typical appetite.
The height of the curve at any point along the horizontal would represent the number of people who have the particular degree of appetite represented by the point below it. There are only a few whose appetite is unusually low (which is why it is described as “unusual”) and a few whose appetite is unusually high. As one moves from either end towards the middle the number of people represented at each point grows larger and therefore the curve grows taller. The middle represents a typical sexual appetite and contains the largest number of individuals, which is why it is described as “typical.”
The single bell curve depicted above represents the human population at large, both male and female. One might, however, depict the range for the male and female populations separately, using two curves on the same graph. They might look like this:
Note that on this graph the men’s curve is slightly rightward of the women’s, suggesting that the typical male has a slightly greater sexual appetite than the typical female. The small variation depicted on this graph and the large overlap between men and women would allow that, on an individual basis, there would be a substantial number of individual women whose appetite is greater than a substantial number of individual men. If the above graph were accurate it would allow for the personal experiences that you have described, while at the same time, allowing the statement that “men want sex more than women” to be accurate with respect to the male population at large .
In reality the divergence between the sexual appetites of men and women could be much wider…
…or it could be narrower. The two curves might actually converge, which would suggest that the range of sexual desire is identical for both men and women.
The first double curve, depicting a narrow divergence, reflects my best judgement as to actual reality, based upon my experience and observation.
A substantial portion of your essay describes conditions and circumstances such as illness or distress that might reduce an individual’s sexual appetite. While that is a worthwhile topic, it is a topic that is entirely distinct from comparing the general differences in sexual appetite between the male and female populations. Populations should be compared based on the typical, or normal circumstances of their individual members, while controlling for intervening circumstances such as illness or distress.
A valid comparison of the difference in sexual appetites between male and female populations would compare the behavior of male and female populations whose members are unencumbered by extraneous, intervening circumstances such as illness or distress. A scientific study comparing sexual appetites would control for such extraneous circumstances.
Let us suppose that the narrowly diverging “bell” curves shown above are depicting an accurate representation of reality. One might then wonder whether such a narrow divergence would be significant in its influence upon human affairs.
A small difference in the range of sexual appetite between men and women as depicted in the double bell curve that is displayed above, may result in a substantial portion of the male population experiencing sexual access to women as a scarce resource. How might the small difference apply to women? Observation suggests that women experience a surplus of unwanted, uninvited sexual attention which causes them significant distress. This is evidenced by, among other things, the existence of the Me Too Inquisition:
Considering that male and female humans differ in the physical configuration of their sexual apparatus, it is likely that they experience sexual intercourse differently from each other. It is possible that the difference in experience could be perceived as a difference in sexual appetite.
Expressions such as…
“…men only want one thing.”
…or…
“…It’s all they think about, it’s all they want…”
…are expressions of hyperbole. They are not intended to be taken literally. People can observe that men tend to pursue sexual access to women aggressively and express that observation in exaggerated form.
A small offset in the range of sexual appetites between the male and female populations can create a significant gap in sexual availability between the two sexes. Men may experience sexual access as a scarce resource while women may experience a surplus of unwanted, uninvited sexual attention causing them significant distress. At the same time, a large overlap in the two ranges can allow for a substantial number of exceptions for individual couples in individual instances.
If it is true that men, collectively, want more sex (or want sex more) than women, then it would be true whether anyone says so or not. It would be true even if speaking that truth upsets some people. Those who perceive it to be true will continue to say so.