That's why they are leading a 450-strong group of Israeli soldiers who won't fight in Gaza or the West Bank, reports correspondent Bob Simon, who interviewed the two in Jerusalem and Tel Aviv for 60 Minutes.
Members of the group are considered heroes by some and traitors by others.
"I felt like what I was doing was wrong," says Iczkovics. "Our presence there simply causes an impossible situation for their normal life." The two discussed their reservations among other soldiers and eventually more joined their movement to refuse to fight in the Occupied Territories.
Amit Mashiah tells Simon of a confrontation with an old Palestinian woman an incident that he said helped convince him to become a Refusenik.
"There was an old lady who ran to me and spat in my face. It's a dangerous situation. You've got your soldiers behind you seeing you've been spat in the face and what do you do?" Mashiah asks. He tells Simon that he "shoved her real hard," and says it was worse for him to shove her than it was to have been spat upon. "It was a terrible thing to do," he says.
The Refuseniks have caused no shortage of soldiers in Israel. In fact, many more volunteers have emerged since the Palestinian suicide bombings were stepped up. Their numbers are small, but because many come from elite units, they must be taken seriously, says Dr. Yaron Ezrahi, a political scientist. "The leadership cannot afford to ignore [Refuseniks]," says Ezrahi, who has served as a strategic analyst for the Israeli Army chief of staff. "My impression was that the leaders of the Israeli Army are definitely taking this message very…seriously."
But a member of Prime Minister Ariel Sharon's cabinet says that among the Israeli people, the Refuseniks are an aberration, an embarrassment to Israel. "They are objectors without any conscience," says Limor Livnat. "I believe that the vast majority of Israelis really believe that now we have to…defend ourselves…make sure that there will be no bombers any more."