Evron was born in Jerusalem. He attended Herzliya Hebrew High School and Hebrew University. Evron's family had lived in Palestine since the early nineteenth century; he is the great-grandson of Yoel Moshe Salomon, one of the founders of Petah Tikva. He was a member of Lehi and the Canaanite movement early in his life and remains critical of Zionism and supportive of some of Canaanism's tenets. In 1956 he co-founded the political group Semitic Action. His writings were published in Semitic Action's journal Etgar and in Tzipor HaNefesh, a paper edited by Amos Kenan and Dahn Ben-Amotz. He worked for Haaretz from 1956 to 1964 and for Yediot Aharonot from 1964 to 1992. At Yediot, Evron wrote a column which appeared on the same page as Kenan's; their page in the paper was given the satirical nickname "Fatahland" in reference to their perceived sympathy for the Palestinians. He also translated books by Bertrand Russell and Edith Nesbit into Hebrew. Evron was the director of the Beit Zvi theater school from 1970 until 1979. He is on the editorial board of the Palestine-Israel Journal.
- מידה של חירות (Midah shel Herut), 1975
- החשבון הלאומי (HaHeshbon Haleumi, A National Reckoning), 1988
- Jewish State or Israeli Nation?, Indiana University Press, 1995. (An adaptation of HaHeshbon Haleumi)
- Diamond, James S. (1990). "We Are Not One: A Post-Zionist Perspective". Tikkun. 5 (2): 107.
- Norman Finkelstein transcribes Evron's name as such in Finkelstein, Norman (2003). The Holocaust Industry (Second paperback ed.). Verso Books. p. 51.
- Eliason, Marcus (1981-07-12). "Begin remains in command despite wafer-thin election victory". Associated Press. Retrieved 2009-10-31.[dead link]
- Silberstein, Laurence Jay (1999). The Postzionism debates: knowledge and power in Israeli culture. Routledge. p. 69. ISBN 978-0-415-91316-4.
- Twersky, Amos (2009-08-11). "Remembering Amos Kenan". Jewish Telegraphic Agency. Retrieved 2009-10-31.
- אודות בית צבי (in Hebrew). Archived from the original on 2008-12-31.
- "About Us". Palestine-Israel Journal. Retrieved 2012-07-09.
- "Jewish State or Israeli Nation?". Indiana University Press.