There used to be one for each decade, an Arab-Israeli war in 1948, 1956, 1967, 1973 and 1982. Now the eruptions into full-scale confrontation are coming more often, at four- or even three-year intervals: 2006, 2008-2009 and the eight days of November 2012.

The immediate consequence, the hardest and most numbing, is the grief of the bereaved: from this round, some 150 Palestinians and five Israelis dead. Next comes the despair, mixed with a kind of envy: why are the people of Northern Ireland – or South Africa – blessed to have their conflicts behind them, resolved more or less, while Israelis and Palestinians seem fated to keep bleeding, locked in a battle that drags on and on, perhaps till the end of time?

And through it all is the weariness: of those living – and dying – in the conflict most of all, but also of those drawn into it somehow. I feel it myself, a deep fatigue with this struggle, with the actions of both sides and, sometimes especially, with their cheerleaders abroad.

So yes, I'm weary of those who get so much more exercised, so much more excited, by deaths in Gaza than they do by deaths in, say, Syria. An estimated 800 died under Assad during the same eight days of what Israel called Operation Pillar of Defence. But, for some reason, the loss of those lives failed to touch the activists who so rapidly organised the demos and student sit-ins against Israel. You might have heard me make this point before, and you might be weary of it. Well, so am I. I'm tired, too, of the argument that "We hold western nations like Israel to a higher standard", because I see only a fraction of the outrage that's directed at Israel turned on the US – a western nation – for its drone war in Pakistan which has cost an estimated 3,000 lives, nearly 900 of them civilians, since 2004.

I'm tired of those who like to pretend that Israel attacked unprovoked, as if there had been no rockets fired from Gaza, as if Hamas was peacefully minding its own business, a Mediterranean Sweden, until Israel randomly lashed out. I'm tired of having to ask whether any government anywhere would really let one million of its citizens be confined to bomb shelters while missiles rained down. I'm weary of having to point out that, yes, occupied peoples do have a right to resist, but that right does not extend to taking deliberate aim at civilian targets – schools and villages – which is where all but a handful of Gaza's rockets were directed.

And I'm especially tired that so many otherwise smart, sophisticated people apparently struggle to talk about Israel-Palestine without reaching, even unwittingly, for the dog-eared lexicon of anti-Jewish cliche, casting Israeli leaders as supremacists driven by a (misunderstood) notion of Jews as "chosen people" or, hoarier still, as international puppet-masters. It pains me that too many fail to realise that while, of course, there is a clear line that separates hostility to Israel and hostility to Jews, that border is porous. Traffic moves across it both ways. Witness the Lazio thugs who bombarded Spurs fans with anti-Jewish chants – "Juden Tottenham" among them – during their match on Thursday night, but also brandished a Free Palestine banner, deployed not to declare solidarity with Gaza but to taunt a club with large Jewish support.

But when I turn in the other direction, to the actions of Israel's leaders, I feel no less exhausted. For I'm weary of an Israel that persists in believing it has a military solution to every problem, that suffers from the impaired vision so well defined by the novelist Amos Oz: "To a man with a hammer, every problem looks like nail." It makes the same mistake again and again. It bombarded Gaza four years ago to "restore deterrence", but it didn't work: the rockets resumed until Israel had to restore deterrence again. Thursday's headline in Haaretz is correct: "Ceasefire agreement almost identical to that reached in Operation Cast Lead." In which case, what was the point? Why did all those people have to die?

The two sides could have used the intervening years to do what former Mossad head Efraim Halevy and several other leading Israeli ex-security figures have long called for: to talk to Hamas. Of course the organisation is brutal, its charter peppered with vile antisemitism, but that's why it is Israel's enemy. If Hamas were the Mothers' Union, the two sides would not be at war. Israel needs to remember that most basic truth: you make peace with your enemies, not your friends.

Yet Israel's own actions constantly make peace ever harder to reach. What message has it now sent? That Hamas, which uses force, gets results – starting with the easing of the Gaza blockade – while Fatah, which practises non-violent diplomacy, gets nothing: the occupation of the West Bank endures. Pillar of Defence has left Fatah's Mahmoud Abbas looking marginalised and irrelevant in the West Bank, while Hamas is strengthened in Gaza.

Partly for that reason, Israel will have to talk to Hamas eventually. But it makes that unavoidable task harder by assassinating layer after layer of Hamas leaders. The military commander Ahmed Ja'abari was no dove, but Israel could do business with him: he was the broker of last year's prisoner exchange for Gilad Shalit. And last week they killed him.

Similarly, the constant expansion of settlements renders ever more complex the eventual task of partitioning historic Palestine into two viable states, one for each people. It also undermines any faith Palestinians might have – and need to have – that two states is the destiny Israel envisages for their shared future.

I'm tired, too, of Israeli public figures who don't merely resort to violence, but seem to revel in it, whether it's the interior minister demanding Israel "send Gaza back to the Middle Ages", or the son of Ariel Sharon advocating that Gaza be flattened, following the principle that underpinned Hiroshima and Nagasaki – both talking as if, after two millennia of Jewish powerlessness, they are drunk on the thrill of wielding power at last.

And I'm weary of the two sides' followers, waving the flags of Israel and Palestine as if these were rival football teams: black v white; my team all good, their team all bad: my team the perennial David, the pure, unblemished victim; their team a permanent Goliath, capable only of wickedness and immune to pain. Those who feel anything at all for these peoples, or even just for one of them, need to end this wearying, deadening obsession with scoring points and winning righteous vindication and focus on the only question that matters: how might these two peoples live?

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