Perhaps he is right. By his mid-20s, however, it was patently clear that Abaaoud would never fulfil his early promise.
After drifting into petty crime and serving a prison sentence, he brought disgrace and heartbreak on his family by journeying to Syria to join Islamic State.
Worse, he spirited his 13-year-old brother, Younes, away with him to become the jihadists' youngest known recruit. When she learned what he had done, his mother, Badi, 64, sank into a depression and fell ill. Racked with shame, she has since returned to live in Morocco.
His father, Omar, 65, is seldom seen on 'International Street' these days, either, and had publicly disowned Abaaoud long before he was revealed to be the evil architect of last weekend's Paris atrocities.
Last autumn, when the family received reports that he had been 'martyred' while fighting for IS, his older sister Yasmina - who has succeeded where her brother so abjectly failed, and now has a good career and lives in an affluent area of Brussels - went further.
"We are praying that he really is dead," was her reaction.
Her prayers, and doubtless those of the West's security forces, went unanswered. As we know, the reports were wrong and 27-year-old Abaaoud was very much alive.
It now seems clear that IS had faked his death as a ruse, so that he could sneak back into Western Europe and plot his murderous terror campaign.
A campaign that appeared to have reached its bloody denouement yesterday, when, according to reports last night, he was killed by French commandos during the dramatic raid on a terrorist lair in the Paris suburb of St Denis.
So how did the bright boy in the blue cap become a fanatical and utterly ruthless terrorist mastermind?
The story starts more than 40 years ago, when his father migrated to Belgium to find work, like thousands of Moroccans at that time.
The once-fine Brussels suburb of Molenbeek had, by then, fallen into ruin, and its white Belgian residents had moved to more salubrious districts, so the incomers were encouraged by the local authority to take over its dilapidated terraces.
With the aid of a loan or grant, neighbours recall, Omar Abaaoud snapped up one of the most prized houses - a three-storey, stone-built corner property, where he and his wife Badi, also of Moroccan stock, raised their children and opened the humble clothes stall.
As he grew more prosperous, he bought a bigger shop in the Rue Prado, now a bustling North African-style shopping bazaar, where traders hawk tagines, spices and chintzy household goods just off the handsome main square.
The young Abaaoud helped out in the store, which offered cheap Western 'fashion' clothes, in contrast to the surrounding shops, selling traditional Muslim robes and head-dresses.
The family weren't religious at all,' a Turkish woman tasked with keeping an eye on their now-empty house told me yesterday.
This view was supported by another former friend, also a Turk, who said the family rarely, if ever, attended any of the district's 22 mosques.
Abaaoud's descent started as he entered his teens.
He began loitering on the streets with troublesome boys, who - unlike him - might have had a reason to simmer with discontent. Boys whose parents did not own a thriving business, and whose futures seemed bleak.
According to a friend who grew up with him, they would smoke cannabis liberally and drink whatever alcohol they could find.
When they needed money to fund these vices, they would steal from shops and sell their booty. Abaaoud also became disruptive at school, which might explain why his father removed him and installed him, at considerable expense, in one of the most exclusive colleges in Brussels, Saint-Pierre College.
To no avail. Within a year, his son had been expelled.
"He was a little jerk," says a former classmate, recalling how he would menace other pupils and harass the teachers, and was discovered to have stolen some wallets.
Wisely or otherwise, however, Abaaoud's father continued to indulge him.
By his early 20s, Omar had set him up in another clothes shop, near his own. He also had use of his father's four-wheel drive car, and later acquired a smart Audi A4.
By now, his favourite haunts lay across the bridge, on the more affluent side of the canal.
He loved to cavort in Brussels' chicest bars and nightclubs, and, since he was good-looking, with swept-back hair and aquiline features, he apparently had many female admirers.
Oddly, however, no one can recall him having a serious girlfriend. "I think he was too busy having a good time, and he liked being with his gang too much," recalls a friend.
Among that 'gang' were brothers Salah and Ibrahim Abdeslam, whom he would later enlist as henchmen in the Paris attacks. Similarly fast-and-loose young tearaways, they lived in an apartment close to the Abaaoud family home.
Salah, a wheeler-dealer who sold fire extinguishers from his flat and ran a bar, was his regular sidekick.
Five years ago, the pair graduated from petty crime to armed robbery and were both sent to jail.
Now came the fateful twist. One that would transform Abaaoud from a playboy and small-time crook into a warped ideologue capable of unfathomable barbarity.
As in France and, to a lesser extent, Britain, the number of ethnic minorities in Belgium's prisons is disproportionately high, and they seethe with discontent.
It makes these cell-blocks ripe breeding grounds for Islamist hatemongers.
And, like Amedy Coulibaly, one of the killers who attacked the offices of Charlie Hebdo magazine and a Jewish supermarket in Paris last January, Abaaoud was radicalised as he served his time.
His mentor was a chillingly plausible young fundamentalist named Fouad Belkacem, the leader of a now banned Brussels organisation called Sharia4Belgium. Its public aim was to create a separate 'Koran state' within Belgium, but it was covertly recruiting gullible Muslim youths for IS.
Belkacem, who was serving a 12-year sentence for belonging to a proscribed terrorist group and 'brainwashing' young people for jihad, clearly did his work well.
For when Abaaoud emerged from Saint Gilles prison, in southern Brussels, the change in him was extraordinary, the Turkish family friend told me.
"I could hardly recognise the Abdelhamid I knew all his life," she said. "He had been smart and clean-shaven, but he came out with a beard and long hair, and he had exchanged his jeans for traditional Arab Muslim robes."
According to his father, speaking through a lawyer yesterday, Abaaoud also took a dim view of his younger brother Younes's Belgian education, believing it was 'too European'.
This, it seems, was his excuse for taking the 13-year-old boy - whose whereabouts are now unknown - with him last year to Syria.
When his sons disappeared from Molenbeek, Omar apparently had no idea where they were, and the family went to the police to report them missing.
But it is believed that Abaaoud eventually called the family to reveal their whereabouts.
His father was dumbstruck by his decision. "Our family owes everything to this country," he said. According to The New York Times, Abaaoud stayed for a time with other French-speaking jihadists, in a grand villa in the IS stronghold of Aleppo. One Belgian expert believes he then joined a Libyan group of fighters, which attracts many Belgian-Moroccan jihadis because of their linguistic and cultural ties, and which has played a major role in spreading terror across Europe. One of its roles, he says, is to dispatch terrorists to sleeper-cells and safe-houses, perhaps including the one raided yesterday in St Denis.
Abaaoud is now known to have slipped in and out of Syria at will.
He gloated in an IS magazine interview about the ease with which he was able to secrete himself from the Middle East and into the heart of Europe - where he plotted a number of attacks, before bringing carnage to Paris.
From phone intercepts and other clues, Belgian security services discovered he was controlled a terrorists' cell in Verviers, eastern Belgium, and was poised to unleash a major atrocity - including adducting and beheading a prominent law enforcement official - when special forces stomed in lat January, killing two of the would-be assassins and capturing a third.
He was by then out of the country, but was later sentenced in absentia to 20 years in prison.
With his warrior looks and narcissistic love of the cameras, he also became a poster-boy for the so-called Islamic State, appearing in grisly videos (one of which shows him heaping bloodied corpses into a trailer-truck) and urging other young Muslims to abandon their "humiliating" Westernised lives to become "martyrs".
Yesterday, as I watched a group of teenagers gather around the TV in a Moroccan café to witness the police and special forces move in on this murderous Pimpernel, I shuddered to wonder how many others might follow his twisted path.
- Daily Mail
