Hillel the Elder teaches (Avot 2:5) that a person should not separate himself from the tzibbur (usually translated as "community" or "congregation"). This is usually understood in physical terms. There is however another dimension to it.
Even if one is quite detached from one’s fellow Jews in both physical and communal terms, one can still be at one with them. The template of the thrice-daily Amidah prayer couches the words of each blessing in the plural, irrespective of whether it is an acknowledgement of God’s existence and His qualities, an expression of gratitude for His kindness, a plea for forgiveness, or a request for the provision of something necessary that is lacking in one’s life. Correlative to this is the need for every Jew who launches into his Amidah to be conscious of the fact that he is only an individual, a small part of a greater entity.
When we pray for good health, for sustenance, for justice, peace or anything else that is encoded into the Amidah, our thoughts should therefore be united with others, our brethren who have the same human needs and requirements. To pray only for one’s own health, or only that of one’s family, but not empathize with the needs of others, is effectively to separate oneself from the tzibbur. This point is stressed by Rabbi Shlomo Wolbe (Alei Shur, sha’ar 3: Tefillat Shemonah Esrei, at p 378, where he cites Rabbi Yisrael Salanter as the source of this idea in general terms but makes no reference to this mishnah).