When looking at how data structures work, it might seem like the worst-case scenarios show us the true complexity. However, that's not always true. Sometimes, only focusing on the worst case can give us a wrong idea about how well a data structure really performs.

First, the average-case behavior can be really different from the worst-case. For example, let’s take hash tables. In the worst case, if there are a lot of collisions, finding something can take up to $O(n)$ time. But in real life, if you use a good hashing function, the average time is usually $O(1)$. This difference might make developers think that hash tables are slow when they are actually very fast most of the time.

Second, the context in which we use a data structure can change how well it works. Take a binary search tree as an example. In the worst case, if the tree is unbalanced, it can take up to $O(n)$ time to find something. But if the data is sorted or added in a balanced way, it usually works at $O(\log n)$. So, if you only think about the worst case, you might think a data structure is not good, even though it works great in many common situations.

Lastly, performance can change in real-life situations. For example, some sorting methods have a worst-case time of $O(n^2)$, like quicksort. But they actually work well most of the time with an average-case behavior of $O(n \log n)$. Things like how the data is arranged can cause differences in performance that the worst-case analysis doesn’t show.

In summary, while looking at the worst-case scenario can be helpful, understanding the average-case behavior and considering how a data structure is used gives us a better idea of its performance. This understanding can help us make better choices in design and efficiency.