It's a little bit confusing. Is it actually comes from stack pop/push terminology?
L.pop([index]) -> item -- remove and return item at index (default last). Raises IndexError if list is empty or index is out of range.
>>> [1,2].pop()
2
Remove and return an arbitrary set element. Raises KeyError if the set is empty.
>>> {1,2}.pop()
1
set.pop does not return the first element. As it clearly says in the help that you quoted, it returns an arbitrary element.
And the reason for this is simple: sets are inherently unordered. There is no meaningful "first" or "last" element.1
1. Since sets are stored as hash tables, it makes sense for both performance reasons and simplicity reasons that set.pop will remove the first element in the hash table, which will often be the same as the first element iterated by the set, but that's not guaranteed. And, in fact, exactly when it's true is different in CPython 3.6 - 3.7 than in 3.3 - 3.5.
{2, 'a'}. That set has no smallest value, and yet pop works just fine.