Rav Yosef cites a braisa: One who has been excommunicated can teach others and they can teach him; he can be hired by others and others can work for him. However, one who has been placed in cherem (one who has been excommunicated twice for thirty days) cannot teach others and they cannot teach him; he cannot be hired by others and others cannot work for him, but he should study by himself in order not to interrupt his studies; he may also make a small store for a source of revenue.
The version of the Rosh states: he should study by himself in order not to lose his learning. The Reshash cites a braisa in Meseches Semochos which states that the reason he should learn is in order not to forget his learning. The Rambam states this reason as well.
A question is asked: Doesn't every Jew have an obligation to study Torah? What is different about a person that has been placed in cherem, that he should study Torah only because of the concern that otherwise he might forget his learning?
A similar question is asked (Igros Moshe Y"D 2:110; B'Toroso Yehegeh p. 185) on the Rambam in Hilchos Talmud Torah (1:10) who states: Until when is a person obligated to study Torah? Until the day he dies. The Rambam cites a verse in the Torah and concludes: And if there is a time that he will not be engrossed in studying Torah, he will forget his learning. Why is that necessary? Would a person be exempt from studying Torah if he is confident that his learning will not be forgotten?
Moed Katan 15a - It seems to me that the Pshat is as follows. It appears from the Gemara that the person who has been put in Cherem has a similar Din to a mourner. Therefore soon after the Gemara stated that an "Avel" is forbidden to learn Torah, the Gemara proceeded to ask what is the Din for a "Muchram". See the Hago'os Ashrei in the name of the Yerushalmi which states that even the "Menudeh", who our Gemara states is allowed to learn, is only allowed to learn things which he is not accustomed to, because he does not enjoy and derive simcha from this. See the Ritva here who writes that this is the reason why an Avel is not allowed to learn Torah, because it makes him happy (in the same way that the Gemara in Ta'anis 30a states that this is the reason one is not allowed to learn on Tisha b'Av).
So the reason the person in Cherem is not allowed to learn Torah is because it makes him happy. However because the period of Cherem could last a while, Chazal did not want to be too stringent if this might lead to the Muchram forgetting his learning (in contrast to "aveilus" which only lasts for a week and only happens to a person a few times in his lifetime). Therefore they permitted (and presumably obliged) the Muchram to learn on his own, which causes less simcha than learning with others. (Possibly this is similar to work which is permitted on Chol Hamoed to prevent a financial loss, and is a Kal v'Chomer from this since Torah is more important than money, and losing Torah is worse than losing money. See also Rosh above 2:1 who discusses an Avel working after the first 3 days to prevent a financial loss)
See also Halichos Shlomo (Tefilah chapter 7 #58 in the name of R. Shlomo Zalman Auerbach zt'l) who proves from the Ritva here (DH Avel) that an Avel has a total exemption from learning Torah but merely is permitted (but not obliged) to learn sad parts of Torah. Therefore I think your comparison to what the Igros Moshe and b'Toraso Yehegeh learn in the Rambam can be refuted, because an Avel is totally exempt from learning so we can say that a Muchram is equivalent to an Avel in this respect. Therefore the only reason to oblige him to learn is so that he should not forget his learning. Consequently there is no proof from here that anyone else who is sure he will not forget his learning is exempt, because he does not possess the special exemption of the Avel or the Muchram from the general Mitzvah of Talmud Torah.
KOL TUV
D. Bloom