While capturing Italy first would have given the Allies an advantage in the air, there is no way they could have moved the necessary number of tanks across the Alps to complete the ground war.
The Alps ?
What Alps ?
I tend to agree with that. In the first world war the Allies couldn't even get the infantry across the Alps.
Churchill was a great leader and often very insightful. But he had his mistakes, sometimes big one. Call Italy “The soft underbelly of Europe” was maybe one of the stupidest things he ever said. He was no doubt referring to the Italians. He may not have counted on the Germans invading Italy to keep it from falling (though this was no hard to foresee).