Eitan was born in Kielce, Poland in 1924 to Rivka and Israel Majdobnek, a religious family. They had three daughters and a son. The father had a store for textiles and linoleum, while the mother was a homemaker.
The rest of the family was wiped out in Kielce by the Holocaust. Alter, who had attended elementary school there, managed to survive and reach Switzerland in early 1945. There he studied mechanical engineering, but he did not complete his studies. In 1946, he moved to the Land of Israel and lived with his maternal aunt in Tel Aviv. He worked in the carpentry shop of the Marpish family, while their son, a Lehi member, was imprisoned.
In 1946, he joined Lehi in Tel Aviv. In the youth division, he was involved in putting up posters and conducting surveillance and observation. He soon became an instructor.
When the State was establsiehd, he enlisted in the IDF along with other Lehi members, serving in Battalion 82 of the 8th Brigade, with the rank of first sergeant. He fought in all the battalion’s battles, and after his discharge in 1950, he continued to serve in the reserves through all of Israel’s wars, up to and including the Six-Day War.
In 1950, he married Zehava Schlesinger. They have two children and numerous grandchildren.
Eitan ran a shoe factory for 23 years, then was an independent insurance agent. He enjoyed woodworking and metalwork.