There’s is where you err — **on any statement.**
A Pope is not impeccable — he is human and makes personal mistakes.
The infalibility only comes into play on announcements of faith and morals, either alone or with the Magisterium.
You’re right, it is greatly misunderstood.
Only on matters of faith and morals — OK?
“faith and morals”, a sufficiently flexible term to cover anything, everything and nothing.
“Infallibility”, For all the definitions no one seems to be able to recognize it if or when they hear it unless the one making the statement deems it so.
But unless the one making said statement is making an infallible statement then what they deem infallible may not be so.
Hard to understand? Since the whole idea makes no sense that’s true enough.