Systems tend to oppose their own proper function.
A nice example of this is checking your passport and boarding card at the airport. The comedian Michael McIntyre has a very funny sketch pretending to walk through an airport. Every three or four paces he has an uncontrollable compulsion to check that his passport and boarding card are still in his breast pocket. At one point he thinks he's lost them and goes into a mild panic.
Your passport and boarding card are completely safe in the pocket. They are not going to suddenly jump out of the pocket all by themselves. Gravity is not suddenly going to go into reverse. You're unlikely to start walking around on your hands. Pretty much the only way they're going to get out of that pocket is if you take them out yourself. Which is exactly what you do to check you haven't lost them!
On more than one occasion I've seen someone unknowingly drop their boarding card while checking they still have it. This is Le Chatelier. You have a goal in mind, you act to achieve that goal, and your action creates the opposite effect!
So now you know about Le Chatelier. You know that the time you're most likely to lose your boarding card is when you check whether you've lost it. So immediately after checking it you'll remember this blog and start to worry you lost it when you checked it. You'll probably have to check it again. Very soon you'll be checking it every three or four paces like Michael McIntyre. And of course, the more you check it the more likely you are to lose it! Le Chatelier again!
UDPATE: Losing your boarding card is NOT an example of Le Chatelier's Principle. It's an example of a different Systems Law: The Law Of Unintended Consequences! See Le Chatelier's Principle Revisited for what Le Chatelier's Principle really is (I think!)