Ave Civitas,
I am a writer of historical fiction, and so I speculate on what could have caused things to happen.
Since no one wrote down what Atilla thought, all we can to is speculate.
Here are my thoughts on why Atilla quit on his advance into Italy.
In Atilla's invasion of Italia the Huns comprised only a small portion (percentage) of the troops available to Atilla.
The Huns were settled in the plains between the Danube and Transylvania.
In his invasion of Gaul where Aetius cleaned his clock for him, there are few mentions of Hunnic cavalry, where in earlier encounters with the Huns the horsemen played a major enough role to be mentioned.
Where Pope Leo met Atilla was pretty far north in Italy. I asked myself this, If the Pope were in Rome and Atilla were sweeping down into Italy, how did Leo get so far north so quickly?
All I could think of was that Atilla wasn't moving very fast. The Pope wasn't notified by short-wave, so some messenger had to ride down, the Pope had to decide what to to, then the Pope had to go north to meet the Hun.
Furthermore, Summer was well on its was and disease must have been dogging his army too. He was in a hurry to get out of Italy and back north before winter closed the Julian Alps.
Lastly, If he had continued south Aetius, who gave him a whipping in Gaul would have crossed the Alps and he would have been trapped in the boot of Italy.
If he knew anything of history he knew that Radagaisus got caught and whipped and killed too, by another good Roman general (Stilicho). He surely did not want that happening again.
By 450 most of Rome's forces were mounted (mounted cavalry and mounted infantry) where Atilla's weren't anymore. The Romans could (and did in Gaul) outmaneuver him.
Just something to think about.
Lothia