Well, there is no clean cut explanation.

Historically the Duchy of Savoia (mainly centered in Piedmont, capital Turin), was the more expansionist Italian state from the late seventeenth century onward.

The dukes played an active role in all the European wars of the period, shifting their alliance between France and Austria, expanding their territory eastward toward Milan and acquiring Sicily and the title o King (Sicily was later exchanged with Sardinia).

So it was already their long time goal to acquire the duchy of Milan.

There were also other factors: it was the more independent minded Italian state, and also the more open to external influences; it certainly had the more advanced and powerful military at the time (not counting the Austrian garrisons). Milan was maybe a more advanced city, but as it was under Austrian rule (along with Lombardy and Veneto), it could not be a fulcrum for independence (there was a revolt in 1848 where the city expelled the Austrian garrison, but it was short lived, and anyway it immediately asked for military support from Piedmont).

Regarding the other states the duchy of Parma, Modena and Tuscany were closely aligned with Austria; the Pope was not interested in territorial expansion, and this also limited any ambitions from the Kingdom of Naples and Sicily (who could not well invade the territory of the Pope).

At the time a complete takeover of Italy by Piedmont was not a given. There were many other hypothesis, like a federation of independent states, with the expulsion of the Austrians, the duke of Piedmont as the Military commander and the Pope as the president of the federation.

After the war of 1859 actually there was no impetus for further expansion from the duke of Savoia, Vittorio Emanuele II; he had gained the duchy of Milan from the Austrians and modern Emilia-Romagna and Tuscany by plebiscite, and he was pretty satisfied. There were proposals for a federation of three states, north Italy under the Savoia in the north, the Pope in the center and the Bourbon in the south.

But then Garibaldi mounted its expedition and conquered the Kingdom of Naples and Sicily with an army of volunteers. At this point Piedmont intervened, as it had no wish for the potential establishment of a republic in the south, and the kingdom of Italy was formed.

So there was more than a factor in play:

• the dynastic impetus of the Savoia to expand, playing the French and the Austrians one against the other

• a strong desire of a large part of the elites of the various Italian states to expel the Austrians and to form some sort of united entity in Italy, with the awareness that only the Savoia had in practice the inclination and the capability to push for this same objective

• the relative fragility of the governments of the other states once the protection of the status quo by the Austrians was removed