How did Chazal know that 'drop exudes from the brain and develops into semen'?

Since this has been a recent theme, and since on parashat Tazria I already discussed the midrash on how to have male children, and Chizkuni's recommendation of how to have male children:

As an example of lack of knowledge of contemporary science leading to rather silly statements, I put forth the following from Rabbi Aharon Feldman's article (presumably also in his book, Eye of the Storm) demonstrating that Chazal knew scientific facts via ruach hakodesh. He writes:

How did they know that "a drop exudes from the brain and develops into semen³⁵" without having known that the pituitary gland, located at the base of the brain, emits a hormone which controls the production of semen? None of this could have been discovered by experimentation. Either they had a tradition directly teaching them these facts, or they knew them by applying principles which were part of the Oral Torah regarding the inner workings of the world. 

35: Source from Kabbala works cited many places, as in Kehillas Yaakov (by the author of Melo Haro’im), Erech Holada.

There are, of course, a number of "problems" with this assertion. Forget whether sources from Kabbalistic works = Chazal. Forget for a moment that "a drop exudes from the brain and develops into semen" is the NOT the exact equivalent of a pituitary gland having influence on the production of semen, such that this is a kvetch and a teretz rather than inspirational proof of Chazal's knowledge stemming from a Divine source.

How did they know? Well, how did Aristotle know?? How did the Pythagoreans know?? After all, all this could not be discovered by experimentation!

And yet, to cite Wikipedia, which in turn cites more reputable sources:

Additionally, "Aristotle tells us that the region round the eyes was the region of the head most fruitful of seed ("most seedy" σπερματικώτατος), pointing to generally recognised effects upon the eyes of sexual indulgence and to practices which imply that seed comes from liquid in the region of the eyes."^[22] This may be explained by the belief of the Pythagoreans that "semen is a drop of the brain [τὸ δε σπέρμα εἶναι σταγόνα ἐγκέφαλου]."^[23] 

This is also likely the source of the idea that Athena was born directly out of Zeus' brain.

Rabbi Feldman was presumably unaware that the Pythagoreans claimed that "semen is a drop of the brain". Otherwise, he surely would not have cited it as evidence of clear scientific truth, which must have stemmed from Hashem.

So what happened here? Chazal may have relied on ruach hakodesh, or sod Hashem liyreav, or tradition, or darshening pesukim, for some few select statements. But by and large, they relied on contemporary scientific knowledge. One example is that Rav studied for eighteen months under a shepherd to become an expert in eye diseases of animals, so as to be able to pasken in terms of bechorot. (See Sanhedrin 5b.) If the shepherd happened to teach Rav an incorrect fact, this would not reflect poorly on Rav. And given the limitations of the time, it would not even necessarily reflect poorly on the shepherd.

A rationalist, particularly one who has deliberately familiarized himself with some ancient Greek science, would recognize that this is simply Chazal (or perhaps, in this case, some medieval kabbalist), basing himself on ancient Greek science.

But if one assumes that every statement from Chazal, even scientific statements, stem from Hashem, Chazal must be infallible in science. And any error is embarrassing. If so, what does one do with an "absurd" statement like this?

There are a few possibilities. One can take a "pnimiyus" approach. And we would have to see the sources inside to see if it is applicable. Indeed, in this particular instance, it might well be, since after all, this is kabbalah, and, just as in ancient philosophy, the Intellect, the Masculine and Feminine, and impregnation have particular deep meanings.

One can instead adopt an apologetic approach, and search modern science for something, anything, which is approximately similar, and then claim that this is what Chazal surely meant. In this instance, the pituitary gland is located at base of the brain, and it secretes hormones, one of which regulates the production of semen. This is not the same as the semen itself coming from the brain, but we can simply claim that the people back then would not have understood Chazal, and so they cloaked their language. This is a kvetch, and a rather weak teretz.

But if you believe that Chazal were infallible in matters of science, then this is not apologetics! This is not weak and not forced. It is inspiring. I don't know whether this is used in kiruv seminars to inspire people, but I would not be surprised. And so, the weakness becomes a strength. And if this is a strength, then this is something to attack those who follow in the path laid out by Rabbi Avraham the son of the Rambam, for how could Chazal have known my kvetched interpretation which accords with modern science?

For a more recent example of this, in March of this year, Rabbi Natan Slifkin wrote about kidneys, as the seat of the intellect. A gemara states:

The Rabbis taught: The kidneys advise, the heart considers, the tongue articulates, the mouth finishes, the esophagus brings in all kinds of food, the windpipe gives sound, the lungs absorb all kinds of fluids, the liver causes anger, the gallbladder secretes a drop into it and calms it, the spleen laughs, the gizzard grinds, the stomach [causes] sleep, the nose [causes] wakefulness. (Berachos 61a)

One commenter wrote the following, but it was a common response:

A well-respected physician e-mailed me the following: "There are powerful hormones secreted by the adrenal glands (that are on the kidneys) - the corticosteroids and adrenalin, which undoubtedly have psychological impact." Furthermore, there is in fact a connection with cognition. The Journal Neurology ("the most widely read and highly cited peer-reviewed neurology journal" by the American Academy of Neurology) recently published an article called "The brain and the kidney connection: A model of accelerated vascular cognitive impairment" - see here: http://www.neurology.org/cgi/reprint/73/12/916. It's now clear that there is a connection between the brain and cognition. "Psychological impact" and general cognitive functioning can surely relate to the connection with our capacity to advise ourselves and others. Do a google scholar, or just a google search, with the words "kidneys cognition" and you'll see more on this topic.

However, having an impact on psychology; or having a negative impact on cognition is not the same as advising, and giving counsel. This is another instance of apologetics, which undoubtedly will eventually turn into evidence that Chazal were infallible in science, rather than the reverse.