What does "non-pathological data" mean?
Pathological data is supposed to be data that makes things go wrong in
some way for your intended computation. It can be called
pathological when it is rare enough in actual uses, so that things
work OK most of the time. This can sometimes be made mathematically
more precise (for example with probabilities), but the use of the
word pathological in often informal.

For example, tomato salad and ketchup are excellent food, except for
pathological people, meaning those people who are allergic to
tomatoes. It can actually kill in some cases.  But people allergic to
tomatoes are very rare so that tomato dishes are considered excellent,
except in pathological cases.

There are many algorithms that, while having a worst case complexity
above the optimal one, are on the average as good or better than worst
case optimal algorithm. If you compare quicksort and merge sort,
quicksort is time $O(n^2)$ while merge sort is $O(n \lg n)$ in the worst
case. But people will often use quicksort, because they both are time
$O(n \lg n)$ on average, and the space complexity is $O(\lg n)$ for
quicksort and $O(n)$ for merge sort.

The fact that quicksort is as good on average may be attributed to the
fact that the $O(n^2)$ time complexity actually occurs only on
pathological (implying bad but rare) cases.