Gemara: If people were sitting in the beit midrash (study hall) and a light was brought before them, Beit Shammai say: Everyone makes the beracha himself. Beit Hillel say: One makes a beracha on behalf of the rest, because it says: "With a multitude of the nation, it is grandeur for the King" (Mishlei 14:28). We understand Beit Hillel, for they explain their reason, but what is the reasoning of Beit Shammai? They reasoned that [doing it together] would cause there to be a cessation of study in the beit midrash. Similarly it says in a baraita: In Rabban Gamliel’s study hall, they would not say "marpeh" (you should be healthy) [when they sneezed] due to cessation of study in the beit midrash.


Ein Ayah (8:6): Completeness can be broken into different categories: the completeness of the collective and the completeness of the individual.
The first level is for a person to make serious efforts to be included in the collective. Then, even if he does not reach the level of quality of character making him deserving of great things, he still gains from being part of the collective. There is a very high level that only a few particularly noble people reach, where their high quality is important even as an individual, without the need to be viewed as part of the collective.
Beit Shammai viewed the beracha on light as being connected to the few special individuals whom Torah is capable of bringing to the highest level. About such individuals, we find statements like the following by Chazal. That which is written, "of the stream of your indulgences (adanecha) you shall give them to drink" (Tehillim 36:9) should be read as "Edenecha," implying that every one (great person) receives his own lodgings in Gan Eden according to his [spiritual] honor. It is appropriate for such great people to make the beracha by themselves.
Beit Hillel felt that the beracha is focused on bringing the nation as a whole toward completeness. Therefore, communal involvement in the broadest manner is greatly desired. This is alluded to by the pasuk, "With a multitude of the nation, it is grandeur for the King." Referring to Hashem as King is appropriate because our recognition of Hashem comes through our understanding of our world. In such matters, bringing people together for that purpose is always good. The gemara says that Beit Hillel’s reason is known because "the honor of kings is to investigate a matter" (Mishlei 25:2). In our context, this means that when something is known by a mass of people together it is fit to be understood by all.
Beit Shammai’s idea needs explanation, and that is that we are concerned with the cessation of study in the beit midrash. It is worthwhile for people to know that there is an especially high level which one can obtain through Torah study, which by itself is able to raise a person to a state where he does not need to be connected to the masses in order to reach his desired level. These are the type of rare individuals about whom one can say that the world was created for people like him. The quality of his existence is such that he is considered like a world unto himself.

Ein Ayah (8:7): It is customary to say "marpeh" in order to strengthen the love and cohesiveness of the group. It is appropriate to do so when one is sneezing because that is something that heals the sick (see Berachot 57b). The need to strengthen love based on passing remarks is needed only when a person has not reached a full understanding. When it is reached, being aware of the importance of the welfare of others is a given. Therefore, Beit Shammai put the stress on the continuation of learning, in which case, they did not feel it was necessary to interrupt it for a matter of manners as a part of group dynamics.