Unfortunately all the ones I have in mind are too controversial and would only elicit a negative response. Or in the very least cause upset to some, which would only be counter productive haha! :)
I guess the birthday paradox is one such example (https://en.wikipedia.org/wiki/Birthday_problem) but if you've taken a course in probability theory then it doesn't really seem counter-intuitive.
There's quite a few veridical paradoxes in probability theory
But haha I was just thinking about math stuff at all. More like sociological, biological, systems, anything!