They don't believe that. The Talmud is a commentary and the Rabbis often offer discourse on the what-if's of the Torah. I found an excellent answer from the Nizkor Project:
Aboda Zara 37a. A complete distortion of the text, and as I
understand the book, explicitly prohibited elsewhere. The rabbis
prohibited cohabiting with Gentile women for fear that they would seduce
their husbands away from following the law and into following their
The discussion of Aboda Zara 37a involves the conditions under which
contact with certain bodily secretions causes ritual uncleanliness,
similar to that of Baba Metzia 114b. The law is that a bodily secretion
of a gentile girl less than three years and a day, if touched, does not
cause ritual uncleanliness. The text says _nothing_ about the
permissibility of having sex with such a girl; that is a malicious
conclusion dishonestly presented as if it were a quote.
"Apparently a deliberate misquote. The observation is a technical, physiological
one, regarding the impurities related to genital "flows" as outlined in
Leviticus chapter 15. The Talmudic source argues that since the tearing of the
hymen at that age would be permanent (as distinct from a younger girl whose
hymen the rabbis believed would grow back), she is considered to have reached a
state of physical development that her discharges would be included under the
category of impure flows according to the Biblical purity laws. (The same rule,
by the way, would apply to a Jewish girl). This is of course not a permission to
"violate" the girl, merely a legal definition of her age."
Edit to asker - there is NO "Libbre David". You have been reading web sites that lie about the Talmud. I quote: "Libbre David 37. This is a complete fabrication. No such book exists in the Talmud or in the entire Jewish literature. "
As for Talmud Ketuvot 11b (The citation mentioned is evidently in error. Talmud Yevamot 11b has no relevant passage)
Rav Yehudah said in the name of Rav: A male child who has relations with a female adult causes her to be like one who was injured with a stick... Rava said: This is what was meant - an adult male who has relations with a female child has not done anything because less than this [three years old] is like sticking a finger into an eyeball.
While those unused to these Talmudic discussions might be taken aback by the use of euphemisms, the discussion here relates to the dowry for virgins and non-virgins. It has nothing to do with what acts are allowed, encouraged, forbidden, or discouraged. It is, indeed, ironic that this passage has been manipulated from its original context of a financial discussion into one of a religious discussion. While there are numerous talmudic passages of a religious nature, this one discusses dowries and not forbidden and permitted relations!
The Talmud relates that a virgin is entitled a higher dowry. While the tell-tale sign of virginity is the release of blood due to the breaking of the hymen on the wedding night, there are occasions when the hymen has already been broken such as when the woman suffered an injury. The Talmud here quotes Rav Yehuda in the name of Rav that a sexual act with a male minor is not considered to be a loss of virginity because one of the participants is not fully active. While the female's hymen may have been broken, she has not engaged in what can be classified as a sexual act (although it is certainly child abuse).
The Talmud continues and quotes Rava as saying that a sexual act between a male adult and a female under the age of three is also not considered a loss of virginity (although it is child abuse). Since the girl is too young for her hymen to be broken, she is still considered a virgin.
Nowhere is the Talmud permitting such behavior. Sex outside of a marriage is strictly forbidden (Maimonides, Mishneh Torah, Hilchot Ishut 1:4, Hilchot Na'arah Betulah 2:17; Shulchan Aruch, Even HaEzer 26:1, 177:5) as is this obvious case of child abuse. The Talmud is only discussing ex post facto what would happen if such a case arose.
Reconstructionist Jew - raised Conservative