QUESTION: The Gemara rules that a Ketanah married to a Kohen may eat Terumah, but a Chareshes married to a Kohen may not eat Terumah. (According to some Rishonim, the Gemara refers to Terumah d'Rabanan; see Tosfos to Yevamos 90a, DH v'Ocheles, and Gitin 55a, DH v'Al Ketanah.) The Gemara explains that in the case of a Chareshes, although the Chareshes does nothing wrong when she eats Terumah (since she is not obligated to observe the Mitzvos), the Rabanan prohibited her from eating Terumah, lest people see her as she eats Terumah and mistakenly assume that in the converse situation, where an ordinary woman is married to a Cheresh Kohen, the woman may eat Terumah (which is prohibited mid'Oraisa, since the Kidushin is not valid mid'Oraisa).
Why did the Rabanan not enact the same prohibition in the case of a Ketanah married to a Kohen? In that case, too, there is a concern that people will see the Ketanah eat Terumah and mistakenly assume that when a Katan who is a Kohen marries an adult woman, the woman may eat Terumah, when in truth the Kidushin is not valid mid'Oraisa and the woman certainly is prohibited from eating Terumah.
(a) RASHI (DH Gezeirah) answers that there can be no such case in which a Kohen Katan is married to an adult woman. The Rabanan did not institute Kidushin at all for a Katan, as the Gemara says earlier (112b).
Not all Rishonim accept Rashi's opinion. Some maintain that the Rabanan did institute Kidushin d'Rabanan for a Katan who marries a Gedolah. (Their opinion will be explained below.)
(b) TOSFOS (DH Shema Ya'achil) disagrees with Rashi's answer. Tosfos earlier (62b, DH Samuch) points out that the Gemara praises a person who marries off his children (i.e. daughters and sons) immediately before they reach adulthood. The Gemara there implies that the Rabanan did institute Kidushin for a Katan (see also Tosfos 96b, DH Nasa). When the Gemara (112b) says that the Rabanan did not institute marriage for a Katan, it means that they did not institute a state of Nisu'in which has the full status of marriage for all of the Halachos of marriage (such as the right of the husband to keep the income of the wife). However, they did institute that a Katan is permitted to marry and is not considered to be living with an unmarried woman immorally.
Why, according to Tosfos, did the Rabanan not prohibit a Ketanah married to a Kohen from eating Terumah lest people assume that a Gedolah (an adult woman) married to a Kohen Katan may also eat Terumah?
Tosfos explains that a Katan usually is married off only close to adulthood. Since not much time remains until he reaches adulthood -- at which moment his Kidushin becomes a Kidushin d'Oraisa -- the Rabanan did not deem it necessary to prohibit the Ketanah-wife of a Kohen from eating Terumah lest people think that the Gedolah-wife of a Kohen Katan may eat Terumah in the short amount of time before he reaches adulthood.
(The TESHUVOS HA'RASHBA 4:207 disagrees with Tosfos and sides with Rashi, who maintains that the Rabanan did not mean that a father should marry off his sons before they reach the age of adulthood, but rather immediately after they reach that age. Any relationship they have before they reach adulthood is considered Bi'as Z'nus.)
(c) RABEINU YITZCHAK B'REBBI YEHUDAH, cited by the MAHARIK (Shoresh #32), writes that the father of a Katan may accept Kidushin for his minor son and the Kidushin takes effect mid'Oraisa because of the principle of "Zachin l'Adam she'Lo b'Fanav" -- a person may acquire a benefit on behalf of somebody else while not in his presence. If the Kidushin of the Katan takes effect mid'Oraisa, perhaps there was no need for the Rabanan to prohibit the Ketanah from eating Terumah, because when a Katan is married to a Gedolah she may eat Terumah because the Kidushin is d'Oraisa!
The Acharonim discuss the opinion of Rabeinu Yitzchak at length. Although an acquisition of property may be transacted on behalf of a Katan through the principle of "Zechiyah" (Bava Metzia 72a, Kidushin 42a), and according to some Rishonim (RAN to Kidushin 42a, TOSFOS to Sanhedrin 68b) the Kinyan takes effect mid'Oraisa, the same does not apply to Kidushin. One cannot transact a Kinyan of a wife for a Katan through "Zechiyah" (or even for a Gadol for that matter; see Kidushin 45a and Rashi there).
The MAHARIT (Teshuvos, EH 2:41) cites many proofs against the opinion of Rabeinu Yitzchak, including the Gemara here (112b) which states that the Rabanan did not institute Nisu'in for a Katan because there certainly exists no Kidushin d'Oraisa for a Katan. (See also AVNEI MILUIM 1:1 who addresses some of the Maharit's questions.)
The Maharit concludes that even Rabeinu Yitzchak himself does not mean that a Katan can become married as a minor with Kidushin d'Oraisa through the father's ability of "Zocheh she'Lo b'Fanav." Rather, he means that the father may accept the money for the Kidushin while his son is a Katan in order for the Kidushin to take effect mid'Oraisa when his son reaches adulthood -- if his son expresses interest in the Kidushin at that point. (He compares this opinion to the Gemara in Kesuvos (11a) which allows Beis Din to perform conversion for a Katan. The conversion takes effect at the time the convert reaches adulthood and consents to the conversion.) Accordingly, even Rabeinu Yitzchak agrees that there is no Kidushin d'Oraisa for a Katan.
The RASHBA (109b) proposes a similar logic with regard to a Ketanah. He writes that when a father accepts Kidushin for his Ketanah daughter, as soon as she reaches adulthood the Kidushin becomes d'Oraisa. The money that the father accepted when she was a Ketanah was intended for the purpose of making Kidushin take effect with the daughter from the moment she becomes a Gedolah, if she consents to the Kidushin at that point.