Not so simple in my case — and until I moved to Israel in 1985 to take up my post as Middle East correspondent for The Observer, it wasn’t a question I had ever been asked. (Well, with one exception, but we’ll come to that in a moment.)

In Israel, however, I was asked almost on a daily basis. And it forced me to confront an issue that until then hadn’t been an issue at all.

I describe my family background in my newly-published memoir, Is Anything Happening? My parents were both refugees from Nazi Germany. They came from non-religious families; in fact, my father and his three siblings had all been confirmed into the Lutheran church. None of which, of course, made any difference to the Nazis.

So I was brought up in the most secular household imaginable — no barmitzvah, no Hebrew lessons, the first time I entered a synagogue was the day I got married in one. (My wife is Jewish.)

And that is where I had to answer two tricky questions: not only ‘Are you Jewish?’, but ‘Can you prove it?’

Fortunately, my mother, on whom the answer depended, was able to dig out her old German passport. And fortunately (from my point of view, although certainly not from hers at the time it was issued), it had a very large J stamped on it.

J for Jew.

So my Jewish identity was established to the satisfaction of the rabbi by means of a Nazi document. Am I Jewish? Well, the Nazis said my mother was: will that do?

As a foreign correspondent working in Israel in the 1980s, before the first Palestinian intifada, or uprising, I lived a privileged life. I could be talking to militant West Bank settlers in the morning, and to Palestinians in a squalid refugee camp a couple of miles away in the afternoon. There was no separation wall, and crossing the Green Line was simply a matter of waving a press pass and driving a car with Israeli registration plates.

Unlike the vast majority of Israelis and Palestinians, I got to know what both their worlds looked like. I could buy my vegetables in the Mahane Yehuda market in west Jerusalem, and my freshly roasted coffee on Salah Al-Din Street in east Jerusalem. Breakfast at a café on Ben Yehuda Street and lunch in Jericho or Ramallah.

I learned to see Israel through two very different sets of lenses. And I learned to appreciate the wisdom of Atticus Finch, the lawyer-hero in Harper Lee’s To Kill A Mockingbird: “You never really understand a person until you consider things from his point of view…until you climb into his skin and walk around in it.”

My maternal grandmother had been deported from Breslau (now Wrocław) and shot by a Nazi death squad in Lithuania in November 1941. So visiting the Holocaust memorial at Yad Vashem was a deeply personal experience. (It was even more personal when, many years later, I stood on the very spot where my grandmother had been murdered.)

I also walked through the grounds of Kfar Shaul psychiatric hospital, where you can still see the remains of the Arab village of Deir Yassin, scene of the one of the most infamous massacres by Jewish fighters in 1948. To get there from Yad Vashem takes no more than fifteen minutes by car, yet the traumas the two sites represent are separated by a seemingly unbridgeable gulf.

I have been reporting from, and visiting, Israel for more than thirty years, and it has become ever more difficult, even for foreign reporters, to cross from one side of that gulf to the other. In October 2000, at the outbreak of the second Palestinian intifada, I was in Nazareth, just after the killing by Israeli police of 13 Arab Israelis and widespread anti-Arab attacks by Jewish mobs. I wrote at the time: “The streets are in charge. Vengeance is in the air…I have never felt so fearful for the future of this blood-soaked region.”

My conclusion? It may surprise you: that in retrospect, the establishment of the state of Israel in 1948 may well have been a mistake. This does not mean that I think Israel should be wiped off the face of the map, or that the Jews who live there should be expelled. But to me, the Zionist dream of a homeland in which Jews could live in safety has turned out to be a chimera. For the nearly seventy years of its existence, Israel has been under constant threat. More than half the world’s Jews still choose to live elsewhere, most of them in the US, where they are far safer than their Israeli cousins have ever been.

Antisemitism has thrived and prospered over the past seven decades on a narrative built largely around the “theft” of Arab lands by Zionist colonisers. Its origins long pre-date the establishment of Israel, but the deep antipathy towards Jews among millions of today’s Muslims surely stems overwhelmingly from the founding of the Jewish state.

Israel exists and will not, under any imaginable circumstances, be de-existed. But by trying to climb into Palestinian skin and walking around in it, I believe it is possible to move towards a new starting point for a discussion about potential solutions. Why not start with a recognition that both Jews and Palestinians have suffered immense trauma?

Why not echo the words of the Queen on her historic visit to the Irish Republic in 2011: “The relationship has not always been straightforward, nor has the record over the centuries been entirely benign…With the benefit of historical hindsight, we can all see things which we would wish had been done differently or not at all.”

If Israelis could bring themselves to acknowledge the trauma caused by the establishment of their state, and if Palestinians could bring themselves to acknowledge the reality of the Holocaust and the suffering caused by hundreds of bomb, rocket and knife attacks on Israelis, it is possible to envisage the possibility of a new beginning. Not aimed at a two-state solution, which has been rendered obsolete by fifty years of settlement-building, but perhaps at a single, federal state in which two peoples share not only a land but also a state.

As someone with a heritage that, bizarrely, entitles me to both German and Israeli citizenship, and whose grandmother was murdered by the Nazis, I refuse to accept that the Israel-Palestine conflict cannot be resolved.

Jews are said to be born pessimists. I, however, insist on being an optimist. So perhaps I’m not Jewish after all.

Robin Lustig’s memoir, Is Anything Happening? is published by Biteback, price £20.