The Gemara says that one is permitted to kill lice on Shabbos because they spontaneously generate:
Rabbi Eliezer said: One who kills a louse on Shabbos is like one who kills a camel on Shabbos (and has violated Shabbos)… Rav Yosef said: The Rabbis disagree with Rabbi Eliezer in the case of lice, which do not reproduce… (Shabbos 107b)
The Rabbis believed that lice “do not reproduce” – that is to say, they do not hatch from eggs laid by other lice. The medieval and later authorities explain that lice are instead generated from sweat. Accordingly, they are not considered to be life-forms like other animals and they may be killed on Shabbos. The Talmud proceeds to question this, based on a statement that seemingly acknowledges the fact that lice hatch from eggs:
Abaye said: And do lice not reproduce? Surely it was said, “God sits and sustains from the eggs of lice to the horns of aurochsen?” (which shows that lice come from eggs)?
The Talmud responds that this statement should be understood differently and does not in fact mean that lice reproduce in the “eggs of lice”:
– That refers to a species which is called “eggs of lice.”
There are many questions and controversies surrounding this passage, which I deal with at great length in my book Sacred Monsters. Here, I want to focus on one question: the strange nature of the last line of the Talmud cited above. As usually understood, it means that the Talmud is responding that the statement about God sustaining the “eggs of lice” does not actually refer to eggs of lice, but rather to a type of insect which is called “eggs of lice.” This seems extremely strange, to say the least! Why would an insect be called “eggs of lice”? Wouldn’t it be much more reasonable to assume that the phrase really does refer to eggs of lice? Furthermore, the beginning of that statement speaks of the God sustaining “the horns of aurochsen,” which are appendages of an animal rather than a type of animal. Accordingly, the last part of the statement would also be describing the appendages of an animal rather than a type of animal. It thus seems very strange for the Talmud to claim that “eggs of lice” are a type of insect!
Another question that people have on this topic is that nits – lice eggs – are not all that tiny. Certainly they can be seen with the naked eye, albeit with some difficulty. Did people really not know about them?
The truth is that if we look at another section of the Talmud, we find an explicit discussion about nits. In a section relating to the law that a nazir may not have a haircut, the Talmud seeks to determine whether hair grows from the tip or from the root. One argument is based on the position of something called “inba” on a hair as it grows:
Does a hair grow from the root or from the tip? …Let us bring a proof from a live inba, which remains at the root of the hair [as it grows]; if you were to say that a hair grows from its root, then the inba should end up at the tip of the hair!
No, one could still say that it grows from the root, and because the inba is alive, it keeps moving down [as the hair grows].
Let us bring a proof from a dead inba, which is at the tip of a hair; if you were to say that a hair grows from its tip, then the inba should be at the root of the hair!
No, one could still say that it grows from the tip, and because the inba has no strength [to grip], it slides along it. (Nazir 39a)
This inba is clearly a nit, and we thus see that Sages of the Talmud had observed nits. So why did they state that lice spontaneously generate? And why did they redefine “eggs of lice” to refer to a species of insect?
In order to answer these questions, let us take a look at what people in the ancient world thought about lice. Aristotle has a fascinating discussion in which he makes it clear that he had seen nits, and he even knew that lice laid them. What he did not know was that lice also hatch from them. Rather, nits were thought to be merely the useless result of two spontaneously-generating lice mating with each other:
But whenever creatures are spontaneously generated, either in other animals, in the soil, or on plants, or in the parts of these, and when such are generated male and female, then from the copulation of such spontaneously generated males and females there is generated a something – a something never identical in shape with the parents, but a something imperfect. For instance, the issue of copulation in lice is nits; in flies, grubs; in fleas, grubs egg-like in shape; and from these issues the parent-species is never reproduced, nor is any animal produced at all, but the like nondescripts only. (Aristotle, History of Animals, Book V, Part 1)
If this is how people thought of lice, then our questions are answered. Rashi states that the “eggs of lice” of tractate Shabbos are the inba of tractate Nazir Accordingly, when the Talmud explains that the statement, “God sits and sustains from the eggs of lice to the horns of aurochsen” refers to a species called “eggs of lice,” it does not mean that there is a species of insect called “eggs of lice.” Rather, it is referring to nits – actual lice eggs. It is stating that they are a distinct entity, that are laid by lice, but not from which lice actually hatch. The Talmud is saying that they are called “eggs of lice” because they are egg-shaped organisms that are laid by lice – but they do not hatch into lice, and thus, according to the Talmud, it is still correct to state that lice spontaneously generate.
Some people have a hard time accepting this, because to their minds, it seems absurd to recognize that lice lay eggs but do not hatch from them; to attribute this belief to Chazal is, in their view, accusing Chazal of being "foolish," heaven forbid. However, they are committing a common error of anachronism. That which seems "obvious" to us today is not at all necessarily "obvious" to people in different eras. Examples of this are legion. But in this case, there's a simple rejoinder to be made: Aristotle was certainly a very, very intelligent and knowledgeable person, and yet he believed that lice lay "eggs" but do not hatch from them.
 Ba’al Halachos Gedolos; Rambam, Hilchos Shabbos 11:3; Rashba, Commentary to Shabbos 12a; Mishnah Berurah 316:38.
 Rashi to Avodah Zarah 3b, s.v. beitzei kinnim, and Rashi to Nazir 39a.