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The Talmud is very complicated, not every statement is a law, sometimes it is a commentary or the opinion of a certain Rabbi, sometimes a stipulation or refutation, however the quotes below should give you a good idea about Talmudic reasoning on certain issues.
According to the Talmud in the book of Sanhedrin 59a, in the opinion of Rabbi Johanan, a non-Jew who learns the Torah should be killed, unless they are converting to Judaism or are learning the special laws which pertain to the Ger Toshab (The Noahide Laws). Footnote 3 to the passage is very forward as to the reason for this: “it is suggested that R. Johanan feared the knowledge of Gentiles in matters of Jurisprudence, as they would use it against the Jews in their opponents’ courts.” In Abodah Zarah 26a – 26b it is the concurrent opinion of both Rabbi Johanan and Rabbi Abbahu that “informers and apostates” also known as “mosers” maybe thrown into a pit to die; this is unlike non-Jews who can only be abandoned in a pit to die, but not thrown in. The Jewish Encyclopedia further details that one who teaches the Talmud to a Non-Jew should be killed (which they brush of as an idiom). It is little wonder why Jews would fear non-Jews gaining an understanding of their laws, especially since Jewish Noahide Law gives non-Jews secondary legal status and prohibits them from practicing their own religion in pain of death.
NON-JEWS WHO LEARN THE TORAH SHOULD BE KILLED UNLESS THEY ARE CONVERTING OR HAVE ACCEPTED THE POSITION OF A GER TOSHAV (NOAHIDE)
R. Johanan said: A heathen who studies the Torah deserves death, for it is written, Moses commanded us a law for an inheritance; it is our inheritance, not theirs. Then why is this not included in the Noachian laws? — On the reading morasha [an inheritance] he steals it; on the reading me’orasah [betrothed], he is guilty as one who violates a betrothed maiden, who is stoned. An objection is raised: R. Meir used to say. Whence do we know that even a heathen who studies the Torah is as a High Priest? From the verse, [Ye shall therefore keep my statutes, and my judgments:] which, if man do, he shall live in them. Priests, Levites, and Israelites are not mentioned, but men: hence thou mayest learn that even a heathen who studies the Torah is as a High Priest! — That refers to their own seven laws. - 1962 Soncino Bablonian Talmud, Sanhedrin 59a
Footnote 3: This seems a very strong expression. In the J. E. (loc. cit.) it is suggested that R.Johanan feared the knowledge of Gentiles in matters of Jurisprudence, as they would use it against the Jews in their opponents’ courts…
Footnote 7: It is meritorious for them to study these; but not laws which do not pertain to them.
INFORMERS AND APOSTATES MAY BE THROWN INTO A PIT TO DIE (OTHERS CAN ONLY BE ABANDONED IN A PIT, BUT NOT THROWN IN)
R. Joseph further had in mind to say, in regard to what has been taught that in the case of idolaters and shepherds of small cattle one is not obliged to bring them up [from a pit] though one must not cast them in it — that for payment one is obliged to bring them up on account of ill feeling. Abaye, however, said to him: He could offer such excuses as, ‘I have to run to my boy who is standing on the roof’, or, ‘I have to keep an appointment at the court.’ R. Abbahu recited to R. Johanan: ‘Idolaters and [Jewish] shepherds of small cattle need not be brought up though they must not be cast in, but minim, informers, and apostates may be cast in, and need not be brought up.’ - 1962 Soncino Babylonian Talmud, Abodah Zarah, 26a – 26b
WHOEVER TEACHES A NON-JEW THE LAWS OF JEWS SHOULD BE “KILLED” (FROM THE JEWISH ENCYCLOPEDIA)
Inasmuch as the Jews had their own distinct jurisdiction, it would have been unwise to reveal their laws to the Gentiles, for such knowledge might have operated against the Jews in their opponents’ courts. Hence the Talmud prohibited the teaching to a Gentile of the Torah, “the inheritance of the congregation of Jacob” (Deut. xxxiii. 4). R. Johanan says of one so teaching: “Such a person deserves death” (an idiom used to express indignation). ‘It is like placing an obstacle before the blind” (Sanh. 59a; Hag. 13a). And yet if a Gentile study the Law for the purpose of observing the moral laws of Noah, R. Meir says he is as good as a high priest, and quotes: “Ye shall therefore keep my statutes, and my judgments, which if a man do, he shall live in them” (Lev. xviii. 5). The text does not specify an Israelite or a Levite or a priest, but simply “a man “ -even a Gentile (‘Ab. Zarah 26a). - GENTILE, 1906 Jewish Encyclopedia
MOSERS (INFORMERS) SHOULD BE KILLED
On account of the fact that his deeds frequently caused mischief and even entailed death and destruction, the sages of the Talmud compared the “moser” to a serpent…. According to Talmudic law, the delator was punished with death; and although in general the jurisdiction of the Jewish courts in criminal cases ceased with the destruction of the Jewish commonwealth, in the case of informers the penalty remained in force, those convicted being punished the more severely because they deliberately increased the danger which constantly threatened the people. – MOSER, 1906 Jewish Encyclopedia