Saying "incompatible" is an understatement of course, perhaps a dramatic one (as my title implies -- but I'll get to that later).
A little explanation is in order, at least for the benefit of female readers. Testicles, which have two primary functions -- generating sperm and secreting hormones such testosterone -- are designed to be air cooled. Wikipedia explains:
"In mammals, the testes are located outside of the body, as they are suspended by the spermatic cord and within the scrotum. This is due to the fact that spermatogenesis in mammals is more efficient at a temperature somewhat less than the core body temperature (37°C or 98.6°F for humans). The cremasteric muscle is part of the spermatic cord. When this muscle contracts, the cord is shortened and the testicle is moved closer up toward the body, which provides slightly more warmth to maintain optimal testicular temperature. When the temperature needs to be lowered, the cremasteric muscle relaxes and the testicle is lowered away from the warm body and are able to cool. This phenomenon is known as the cremasteric reflex." -- "Testes", WikipediaWikipedia slyly says spermatogenesis is more efficient when cooler than basal body temperature, but the phrase "more efficient" disguises the real problem: copying errors. If a man's testicles get too hot (or too cold) his sperm doesn't develop properly, becomes damaged and causes birth defects. (It is well known that the vast majority of birth defects in humans are the result of such "copying errors" in the sperm, not in the egg.).
So, if a man's testicles get too hot, the reproductive consequences can be severe. The human body, of course, has an easy solution. When it's cold, muscles pull the testicles up tight into the crotch where the higher temperature of the body warms things up. In milder and especially in hot weather, those same muscles drop the testicles away from the body where they can be air-cooled as the man moves around.
That's where the problem with underwear crops up. Male underwear prevents air-cooling. Even worse, it presses the testicles into the crotch where the heat of the body bakes the little spermazoa, reducing their number and motility, and facilitating copying errors.
Quite honestly, in a sane society men would be encouraged to parade around naked in the summertime. It would be the best way to reduce birth defects, and for that reason alone nudity should be considered a matter of public health. As a matter policy, outdoor areas should be designated clothing-optional. This would have happened long ago, of course, if we didn't live an a religiously insane society, one where the body itself is considered obscene -- where testicles aren't supposed to exist and if they do, they must be kept out of sight in the dark, hot, hidden crotch.
Beyond the known healh risk of male underwear causing birth defects, I suspect (from personal experience) additional adverse consequences. I have observed that when my testicles get too hot for too long, I get a "dead" sort of feeling inside my balls -- a sort of "Eunuch" feeling -- and it's not fun. It makes me feel thwarted and kind of vicious.
It would not surprise me if there is some relationship between that feeling and male violence. Perhaps rapists get that way -- to some extent - because of their underwear. When the testicles get too hot, one feels impotent and the natural substitute for male potency is male power: that is to say, if you lack potency you seek power over others in compensation. (That's an intuition I've long had, and I suspect it's got more than a little truth to it.)
The testicles generate hormones (testosterone and others), so it is not at all a stretch to imagine that a temperature imbalance in a man's balls can lead to a hormone imbalance and, ultimately, to violent behavior.
So, short of becoming a clothing-optional society, what's the solution to the underware problem? I'll make several suggestions.
First off, tighty-whiteys must go. They force the testicles tightly against the crotch, guaranteeing overheating during any season but winter.
Boxer shorts are a better choice, but they still prevent air-cooling. And since pant sytles tend to be tight-crotched nowadays, in practice they are only a modest improvement over tighty-whiteys.
In the hot summer, there is another problem with boxer shorts. Tighty-whiteys at least are cotton, and usually are styled to wrap around the testicles, which puts cotton between the skin of the inner thigh and skin of the testicles. This helps keep the area dryer, at least. With boxer shorts during hot summers, it's not unusual for the testicles' skin to stick sweatily to the inner thigh. Not a fun feeling.
So, in a society that abhors nudity, what to do?
The best solution, it seems to me, is for men to start wearing skirts or kilts. Of course -- without underwear. That allows the cremasteric muscle to do it's thing, raising or lowering the testicles as necessary to keep them at the optimal temperature.
And intuitively, don't we sense that men in kilts and skirts are less prone to violent behavior? Less likely to be rapists? Benign, and yet potent in the one way that counts: full of healthy active little spermazoa growing in their testes.
Another, less public (and less ideal) solution: buy underwear with generous testicle room. Better yet, draw your penis and testicles through the "fly" in your underware so they are on the outside and isolated from your body heat a bit. You can get away with doing this under your pants (no one will ever know) -- or better, do it under your kilt or skirt. You get the benefits of underwear, but also some of the benefits of air-cooling.
In the long run, public health requires us to throw off the old religious insanity about nakedness and embrace a clothing-optional lifestyle. And women should wear the pants in the family, not men.