That's one way of putting it. I believe wiki is taking the King (and Mack-Smith) very much too literally. From my Italian version, Mack Smith isn't really saying that he, Mack Smith, doesn't understand why, nor that it isn't entirely clear why, but that the King, speaking of his abdication "in a rather peculiar manner added that his successor would have been [...] his cousin, the Duke of Aosta, who didn't share his personal disdain for the job of king" (this is my translation from the Italian version - if you have the English original, feel free to add it).

Victor Emmanuel III was a rather particular character in his own right and his relations with his cousin were also peculiar.

What needs to be understood first is that the King spoke of abdication all the time - it was to him a recurrent rhetorical device, a way to set things straight: I wear my crown as a duty, I don't especially like it, and if you like my cousin better, I'll get out of your way. He had said so to his mother before coming to the throne, he had repeated it during his bethrotal to the Princess of Montenegro, again at the time of the intervention, in the days of the march on rome, and so on.

Curiously enough - right at the time when everyone wanted him to get out of the way, during his last months of reign in 1944 - the King was persistent in delaying transfering his powers to his son.

The King of Italy wasn't an imposing man, he was short, of average intellect; competent but dry. His main passion was his enormous collection of coins. His life was frugal, far from the hunting and mistresses of his ancestors. He had been subject to a strict military education which, while it had "built him a character" and infused his mind with all the necessary notions, had also increased his feelings of inadequacy.

Short and mediocre as he was - this famous picture side by side with the King of Belgium - the King's health had improved since his youth, when rumors had circulated that his weakness was to prevent him from coming to the throne. While never official, it's likely he had heard them - so that the idea of being tolerated, not well liked, never loved remained a part of his character. This kind of anecdotes kept circulating around him, involving his desire to avoid the throne, or other more private, such as the time when he had been reprimanded because he didn't want to go out for a walk, for fear that people would look at his stunted skinny legs.

In fairness, such rumors were largely apocriphal, since there was a significant degree of secrecy surrounding the institution of the Crown and people who were directly involved or intimate of the King said very little, and nothing too unfavorable. But they existed and informed to some extent the King's attitude towards those around him.

Now, the Duke of Aosta on the other hand was tall, straight, a few months older than Vittorio Emanuele, himself the son of a King, claimant to the throne of Spain, accomplished horserider, a man of vast ambition and personal pride, married to a Princess of Orleans, daughter of the Count of Paris (not, like the still well liked queen Elena, of the King Nikola of Montenegro).

The Duke of Aosta had all the markings of royalty which Vittorio Emanuele lacked - he was also a thoroughly mediocre man, whose ambition was largely satisfied with surrounding himself of a court of obliquous personalities, of playing a long charade of royal customs (such as his practice of "holding court" in Naples), of earning honors as military commander, up to his ascension to the legendary leader of the "unvanquished" Third Army of the Great War and his promotion to Marshal of Italy in 1926.

Given his stature as military commander, his generosity and proclivity for national and patriotic sentiments, the Duke of Aosta became soon enough the reference figure, at times well beyond his intention or political designs, for every authoritarian, nationalist, strong-man plot of more or less vague and incoherent definition.

So he appeared in 1917 with Cadorna, in 1919 with D'Annunzio, Giardino and Caviglia - in 1922 allegedly the king had revealed that, had he refused to appoint Mussolini, the Fascists and Nationalists were going to replace him ("The Duke of Aosta, the Duke of Aosta, that's what they want!" - he allegedly cried in a certainly dramatized scene).

A few have actually credited these revelations as true explanations of many of the King's political choices (see for instance A. Repaci's La marcia su Roma) - I believe that the special place held by the Duke in Vittorio Emanuele's mind reveals something of the King's need for a crutch, an external form of his own weaknesses and limitations.

I am not sure there is enough to warrant such analysis though - we do have very little on the King, outside from a whole lot of rumors, voices and supposed revelations.

It's also worth remembering that the political crisis of 1915, centered around the intervention and the definition of the Treaty of London, was one between the neutralist forces (which to an extent could be described as "constitutional-moderate" led by Giolitti, in control of a parliamentary majority) and the interventionist ones (which was more prominently influenced by nationalistic themes, and led by the parliamentary minority - sort of - of Prime Minister Salandra). The king's remark could also serve to frame the alternative in these terms: do you want to go to war with me, a constitutional king who respects the parliament, or with the Duke of Aosta, a man who wishes nothing better than to go back to the military governments of the last war with Austria? The exclusion of a boy-king would be an explicit confirmation of the diminution of the parliament's authority under the supposed new king.

Without indulging in any more speculation though, the King used hints at his cousin taking over as recurrent rhetorical devices. And Mack Smith's quote seems to support this view.

As to the other point I mentioned - that the king didn't want to leave his throne to his son in 1944, at least not before he returned to Rome - we should keep in mind that Vittorio Emanuele's understanding of the monarchical institute was that of a king, not that of a commoner.

With the death of his father - assassinated at the turn of the century - it's likely that the King had accepted his duty, whether he liked his job or not, which was a duty towards the House of Savoy, and keeping his House alive and possibly strong was a central concern for the king, which we may risk overlooking under other less "royal" political concerns. So it might be that the King was truly worried of the fate of his House if his throne had been usurped by his taller, less competent cousin - no matter how unlikely the eventuality truly was.