Preacher, historian, economist, moralist, schoolteacher, critic, warrior, imam, emperor. Sometimes you even forgot Barack Obama was the President of the United States of America.

Will his lecture to a carefully chosen audience at Cairo University "re-imagine the world" and heal the wounds of centuries between Muslims and Christians? Will it resolve the Arab-Israeli tragedy after more than 60 years? If words could do the job, perhaps...

It was a clever speech we heard from Obama yesterday, as gentle and as ruthless as any audience could wish for – and we were all his audience. He praised Islam. He loved Islam. He admired Islam. He loved Christianity. And he admired America. Did we know that there were seven million Muslims in America, that there were mosques in every state of the Union, that Morocco was the first nation to recognise the United States and that our duty is to fight against stereotypes of Muslims just as Muslims must fight against stereotypes of America?

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But much of the truth was there, albeit softened to avoid hurting feelings in Israel. To deny the facts of the Jewish Holocaust was "baseless, ignorant and hateful", he said, a remark obviously aimed at Iran. And Israel deserved security and "Palestinians must abandon violence..."

The United States demanded a two-state solution to the Israeli-Palestinian conflict. He told the Israelis there had to be a total end to their colonisation in the West Bank. "The United States does not accept the legitimacy of continued Israeli settlements."

The Palestinians had suffered without a homeland. "The situation for the Palestinian people is intolerable," Obama said and the US would not turn its back on the "legitimate Palestinian aspiration for a state of their own". Israel had to take "concrete steps" to give the Palestinians progress in their daily lives as part of a road to peace. Israel needed to acknowledge Palestinian suffering and the Palestinian right to exist. Wow. Not for a generation has Israel had to take this kind of criticism from a US President. It sounded like the end of the Zionist dream. Did George Bush ever exist?

Alas, he did. Indeed, at times, the Obama address sounded like the Bush General Repair Company, visiting the Muslim world to sweep up mountains of broken chandeliers and shredded flesh. The President of the United States – and this was awesome – admitted his country's failures, its over-reaction to 9/11, its creation of Guantanamo which, Obama reminded us all again, he is closing down. Not bad, Obama...

We got to Iran. One state trying to acquire nuclear weapons would lead to a "dangerous path" for all of us, especially in the Middle East. We must prevent a nuclear arms race. But Iran as a nation must be treated with dignity. More extraordinarily, Obama reminded us that the US had connived to overthrow the democratically elected Mossadeq government of Iran in the Fifties. It was "hard to overcome decades of distrust".

There was more; democracy, women's rights, the economy, a few good quotes from the Koran ("Whoever kills an innocent, it is as if he has killed all mankind".) Governments must respect "all their people" and their minorities. He mentioned the Christian Copts of Egypt; even the Christian Maronites of Lebanon got a look in.

And when Obama said that some governments, "once in power, are ruthless in suppressing the rights of others", there was a roar of applause from the supposedly obedient audience. No wonder the Egyptian government wanted to select which bits of Obama's speech would be suitable for the Egyptian people. They were clearly very, very unhappy with the police-state regime of Hosni Mubarak. Indeed, Obama did not once mention Mubarak's name.

Over and again, one kept saying to oneself: Obama hasn't mentioned Iraq – and then he did ("a war of choice... our combat brigades will be leaving"). But he hasn't mentioned Afghanistan – and then he did ("we do not want to keep our troops in Afghanistan... we will gladly bring every one of our troops home"). When he started talking about the "coalition of 46 countries" in Afghanistan – a very dodgy statistic – he began to sound like his predecessor. And here, of course, we encountered an inevitable problem. As the Palestinian intellectual Marwan Bishara pointed out yesterday, it is easy to be "dazzled" by presidents. This was a dazzling performance. But if one searched the text, there were things missing.

There was no mention – during or after his kindly excoriation of Iran – of Israel's estimated 264 nuclear warheads. He admonished the Palestinians for their violence – for "shooting rockets at sleeping children or blowing up old women in a bus". But there was no mention of Israel's violence in Gaza, just of the "continuing humanitarian crisis in Gaza". Nor was there a mention of Israel's bombing of civilians in Lebanon, of its repeated invasions of Lebanon (17,500 dead in the 1982 invasion alone). Obama told Muslims not to live in the past, but cut the Israelis out of this. The Holocaust loomed out of his speech and he reminded us that he was going to the site of the Buchenwald concentration camp today.

For a man who is sending thousands more US troops into Afghanistan – a certain disaster-to-come in the eyes of Arabs and Westerners – there was something brazen about all this. When he talked about the debt that all Westerners owed to Islam – the "light of learning" in Andalusia, algebra, the magnetic compass, religious tolerance, it was like a cat being gently stroked before a visit to the vet. And the vet, of course, lectured the Muslims on the dangers of extremism, on "cycles of suspicion and discord" – even if America and Islam shared "common principles" which turned out to be "justice, progress and the dignity of all human beings".

There was one merciful omission: a speech of nearly 6,000 words did not include the lethal word "terror". "Terror" or "terrorism" have become punctuation marks for every Israeli government and became part of the obscene grammar of the Bush era.

An intelligent guy, then, Obama. Not exactly Gettysburg. Not exactly Churchill, but not bad. One could only remember Churchill's observations: "Words are easy and many, while great deeds are difficult and rare."