I was flying KLM from the UK to the USA with a short layover in Amsterdam.
Because of delays in the UK, I almost missed my flight. The flight attendant told me my bag wasn't going to make it, but if I walk fast, my gate is just two over.
When I got to the gate, they had already closed the doors, but the counter was opened - I mentioned that my bag was not going to make it, but that's okay. She said, "hold on," got onto her walkie-talkie, and said,
"Yep, that's what I thought: you can't fly if your bag's not going."
I originally thought that it might be a security concern, but that doesn't really make any sense.
Why can't I travel if my luggage doesn't make the connection?
EDIT: I should clarify that I have no beef with KLM - they treated my overnight in Amsterdam professionally and helpfully; I'm just curious what the reason would be.