Rabbi Herschel Schachter
The Torah commands every Jew to be careful not to cause a chilul Hashem. When an individual Jew acts improperly, he disgraces the entire Jewish people, as well as the Jewish religion.
The story is told that on one occasion the local Catholic bishop commented to Hagaon Reb Yitschok Elchanan Spector that one of the major causes of anti-Semitism was the Talmudic statement that "atem kruyim adam ve'ein umos ha'olam keruyim adam". He argued that if the Jews do not consider non-Jews to be human beings, how could Jews expect anything less than animosity from non-Jews.
Reb Yitschok Elchanan explained to the bishop that he had not properly understood the Talmudic statement. What the Rabbis mean to say was the following: In biblical Hebrew there are four terms for a person - ish, enosh, gever, and adam. The first three terms have a different form when used in the plural (anashim, gevarim). The last term - adam remains the same even when used to refer to many men.
With respect to any other individual who murders, steals, or acts improperly, we do not say that his behavior is representative of his entire nation. We would say that that individual is bad, but the rest of the nation as a whole is basically good. We distinguish between gever (in the singular) and gevarim (in the plural); between ish (in the singular) and anashim (in the plural). But with respect to the individual Jew, we call him "adam", used for both the singular and the plural, and assume that the individual is representative of the entire people. Only regarding the Jews is there a principle that "kol Yisroel areivim zeh lazeh". The concept of nationhood only applies to the Jews: "Mi keamcha Yisroel goy echad ba'aretz"; other peoples are called "mishpachos ha'adamah".
Rabeinu Saadia Gaon commented that the uniting force for Jews is the Torah. Other peoples, who have no Torah to bind them together, have no concept of "kahal" (see Talmud Nazir 61b). Any individual Jew who behaves improperly brings disgrace upon his entire nation, as well as upon the entire Jewish religion exactly because we are all one "adam".
The Yerushalmi explains the idea behind the prohibition of nekama (taking revenge) through a moshol: If one was cutting a loaf of bread with a knife in his right hand, and accidentally cut a finger on his left hand, would his left hand slap the right hand out of revenge? Of course not! Both hands belong to one body. So too all Jews constitute "one body". The singular and the plural are both "adam".
G-d tells Avraham, "V'eescha l'goy gadol ... v'nivrechu b'cha kol mishpachos ha'adama" (B'reishis 12:2-3) - "and I will make you into a great nation ... and all of the families of the land will be blessed through you". The term "goy" (nation) is only used when referring to the Jewish people, while the term "mishpacha" (family) is used when referring to other nations (see sefer Eretz Hatzvi siman 17 for a discussion of the halachic implications of this concept regarding determining the genealogy of Jews and non-Jews). Only among the Jews, about whom the same term (adam) is used for both the individual and the entire people, indicating a unique level of oneness and mutual responsibility, is true nationhood achieved, and therefore only regarding us did G-d use the term "goy" (nation).