The Torah refers to Avraham Avinu as "ha'ivri - the Hebrew". Rashi quotes the medrash that the understanding of that expression is that even though the whole world was going in one direction, Avraham Avinu had the courage to go in a totally different direction. Throughout the generations, all of the descendants of Avraham Avinu were known as the Hebrews for the same reason.
In Chumash Bamidbar in Parshas Bahaloscha there are two pesukim that are separated from the rest of the Chumash with the letter nun backwards before and after them. The Medrash Yalkut HaReuvaini points out that nun is the Aramaic word for a fish. The backward nun represents a fish that is able to swim against the tide. The Gemorah in Avoda Zara comments that because kosher fish are coated with scales they have a thick skin and are able to swim against the tide. Non-kosher fish which don't have a coat of scales cannot swim against the tide. The two pesukim separated from the rest of Chumash Bamidbar are "Vayehi binsoah ha'aron" and "Uvenucho yomar". The Jewish people travel from country to country, from continent to continent, from generation to generation, and always take the Torah with them. The Jewish people are the Ivrim (Hebrews) who are always counter-cultural wherever they go; the whole world is going in one direction and the Jews are going in an entirely different direction.
In Parshas Chayey Sara when Avraham Avinu speaks to the non-Jewish community of Chevron he says, "ger v'toshav anochi imachem - I am a stranger and a citizen with you". Rashi points out in the name of the medrash that these two descriptions are contradictory; one who is a citizen is not a stranger. Rav Soloveitchik offered a beautiful interpretation of that pasusuk: the Jewish people are toshavim in this world in the sense that we work along with everyone else to solve all the social, economic, and medical problems of world. The Jews are way less than one percent of the world population and have received over twenty percent of the Nobel Prize winners. The committee that chooses these awards is not made up of Jews. In a very strong sense the Jewish nation is a toshav along with all the other nations of the world to improve the world that we live in. But at the same time, we are a ger - we are always counter cultural. Wherever we go we take the Torah with us, and we are like the kosher fish that swim against the tide.
The Kuzari has a famous line. The philosophers of the Middle-Ages used to divide everything in the world into four categories: animal, vegetable, mineral, and human being. R' Yehudah Ha'levi thinks that Klal Yisroel comprises a fifth category, totally separate from the other four. The non-Jewish residents in Chevron had great respect for Avraham Avinu and offered him the most honorable location to bury Sara Imeinu. Avraham Avinu responded that the Jews are born differently, live differently, die differently, and are buried differently. Avraham found it necessary to designate a separate location (Me'oras Hamachpeilah) as kever Yisroel.
We are all familiar with the emancipation's motto that all men are created equal. The Torah clearly singles out the Jewish people as the Am Hanivchar, i.e. something very different. Rav Soloveitchik once mentioned that he heard from his grandfather - Rav Chaim - that there are different bridges, some are short and some are long. But he thought that it was impossible to build a bridge long enough to bridge the gap between a Jew and a non-Jew.
Every day we recite the beracha, "ozer Yisroel b'gevura", and we have a different beracha ("hanosein la-yoeif koach") where we praise Hashem for giving strength every morning to all human beings. Gevura and koach are not the same as each other. Rav Soloveitchik thought that gevurah refers to heroism; Hashem gives Bnei Yisroel the gevurah to live amongst all the nations and to be an Ivri like Avraham Avinu