I usually don't teach our Data Structures course, but I often give a guest lecture about balanced binary search trees. This comes right after they've learned about plain (unbalanced) binary search trees. Often the previous lesson has ended with an illustration of what happens when values are inserted into the tree in sorted order.
After reviewing that pathological case and how it can easily arise in practice, I dive in and explain how to keep the trees balanced. In my case, I use red-black trees, but the exact choice of balancing scheme isn't critical to my point here. At the end of class, I ask them how much faster they think the balanced trees are than the unbalanced trees. They're shocked when I tell them that, most of the time, the balanced trees are slower than the unbalanced trees. As long as the data arrives in a reasonably random order, the plain binary search trees will actually end up being fairly balanced, without doing any extra work. No mucking around with colors, no rotations—of course the balanced trees are slower!
So why bother?
I tell them that it's like buying car insurance. When you buy car insurance, you hope that you're just throwing your money away. At the end of the year, if you haven't been in any accidents, you're happy to have wasted that money. Why bother? To protect against the uncommon case, to keep one unlucky event from turning into catastrophe. You pay a little bit extra all the time to keep from paying a lot extra every once in a while.