1) THE TYPE OF HALACHAH WHICH THE TANA PREFERS TO TEACH
QUESTION: The Gemara explains that the Mishnah prefers to teach laws derived through a Derashah (and which are not written explicitly in the Torah). The Gemara in Yevamos (2b) states that this is because laws derived by the Rabanan through a Derashah "are beloved" to the Tana. (See also Bava Kama 17b and Bava Basra 108b.)
However, the opposite idea is expressed elsewhere in the Gemara. In Bava Metzia (95b), the Gemara explains that the Mishnah there (94a) mentions only the law which the Torah writes explicitly, and it does not mention the law which is derived through a Derashah. How are these contradictory statements to be reconciled? (MAHARATZ CHAYOS to Bava Metzia 95b)
ANSWER: The MAHARATZ CHAYOS answers that the Mishnah here in Nedarim (and in Yevamos) teaches both Halachos -- that which is derived through a Derashah and that which is written explicitly in the Torah. Its preference for a law derived through a Derashah is expressed by teaching that law first. The Maharatz Chayos explains this preference based on the words of RAV MOSHE KAZIS (in SEFER KIN'AS SOFRIM and as cited by the YAD MALACHI #11), who asks why the Gemara in Yevamos says that "since it is derived through a Derashah, it is beloved" and does not say that it is "more important." He explains that a law which the Rabanan derive through their own toil in applying the methods of Halachic derivation is more cherished and beloved to them because of the effort exerted. Based on this, the Maharatz Chayos explains that where the Tana lists both laws, he prefers to mention the one that is "beloved to him" first. That law, however, is not necessarily more important than a law written explicitly in the Torah; it is merely more beloved. In contrast, the Mishnah in Bava Metzia mentions only one law, and thus it chooses the law which is written explicitly in the Torah, for that law indeed is "more important."
(Although this approach explains why the Mishnah here in Nedarim explains the laws of Yados first, it does not explain why the Gemara says that the Mishnah lists the law that is explicit in the Torah (i.e. Kinuyim) first, and only afterwards lists the law derived from a Derashah. The BEIS YOSEF, in KLALEI HA'GEMARA 3:19, his commentary to Halichos Olam, discusses this question at length. See HALICHOS OLAM there, and see also YAVIN SHEMU'AH there.) (I. Alsheich) (See also Insights to Bava Metzia 95:3.)

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2) "BAL TE'ACHER" OF NEZIRUS
QUESTION: The Gemara explains that the Isur of Bal Te'acher applies to Nezirus in the case of a person who says, "I will not leave the world before I become a Nazir."
Why is that a case of Bal Te'acher of Nezirus? The person did not yet become a Nazir; he only promised to make himself a Nazir at a later time, and his obligation to make himself a Nazir is because his statement was a Shevu'ah or a Neder Mitzvah (one who accepts upon himself to perform a voluntary Mitzvah in the future is bound to keep his word; see Ran to 8a, DH veha'Lo). The Nezirus itself, however, does not obligate him to become a Nazir. Why, then, is this a case of Bal Te'acher of Nezirus? It is merely a case of Bal Te'acher of Neder!
Moreover, why does the Gemara demonstrate Bal Te'acher with this complex case of Nezirus? It should give a simple case in which a person says merely, "I accept upon myself to become a Nazir at a later date." If he delays becoming a Nazir he transgresses Bal Te'acher. (TOSFOS in the name of RABEINU YOSEF)
ANSWERS:
(a) In his first answer, TOSFOS apparently understands that what obligates the person to become a Nazir indeed is a Neder Mitzvah. Nevertheless, it is called "Bal Te'acher" of Nezirus because he made a Neder to perform the Mitzvah of Nezirus. The Gemara's intention may be to teach that Nezirus is considered a Mitzvah such that a resolution to become a Nazir is binding.
Tosfos also addresses the question of why the Gemara demonstrates Bal Te'acher of Nezirus with such a complex case. Tosfos writes that the Gemara actually means to give the simple case. When the person says, "I will not leave the world before I become a Nazir," he means to say, "I accept upon myself to become a Nazir at some point in my life," which is the simple case of accepting upon oneself to become a Nazir. The reason why the Gemara mentions that he specifies that he will become a Nazir during his lifetime is to show clearly that he is not leaving Nezirus as a voluntary option, but that he is obligating himself to become a Nazir.
(b) In his second answer, TOSFOS implies that the statement, "I will not leave the world before I become a Nazir," is the actual Kabalah (acceptance) of Nezirus, but nevertheless the person is not yet required to observe the laws of Nezirus in practice. Normally, one who accepts upon himself to become a Nazir must begin to observe the laws of Nezirus immediately, for thirty consecutive days. However, in the case of the Gemara here, he specified that he will practice the Nezirus any time before he dies, and thus he may choose to begin the observance of the Nezirus at any point in his life, for thirty consecutive days. At the time he chooses to observe his Nezirus, he does not have to accept Nezirus upon himself again by saying, "I hereby accept upon myself to become a Nazir," because the statement he made initially constitutes the formal acceptance of the Nezirus. Hence, when he delays practicing the Nezirus, he indeed is guilty of Bal Te'acher of Nezirus. This also seems to be the intention of the RAN.
A practical difference between these two approaches is whether or not Bal Te'acher applies in the case of a person who says, "I accept with a Neder to be prohibited from eating grapes for thirty days, at some point before I die." According to the first approach, he is not required to refrain from eating grapes at all, since he has not yet accepted upon himself not to eat them. Since there is no Mitzvah to refrain from grapes, his statement does not bind him to accept such a Neder upon himself in the future; he simply may change his mind and not prohibit himself from grapes.
In contrast, according to the Ran, he already made a Neder to refrain from eating grapes when he made his initial statement, and therefore he is obligated to refrain from grapes at some point during his lifetime. (This indeed is the opinion of the Ran later in Nedarim (63a), as the GILYON HA'SHAS points out.)