Flush draw frustration

I can never get over how people play the flush draw. It's second level of an MTT. The blinds are 15/30. Everyone has got just about their starting stack of 2,000 chips. I'm on the button with AQ. I raise up to 100 chips and get 2 callers. The flop comes AQT with 2 spades. It's checked to me and I bet 400 chips. BB goes all-in. I call. BB shows the flush draw and hits. I go out.

What is it about the flush draw that makes people put all their chips into the middle? I can understand it as a semi-bluff. To try and knock the other player off a marginal hand. But, I'd raised pre-flop, overbet the pot with an Ace on the board. That should be a sign of massive strength. If a player goes all-in against that then it's pretty certain he'd get a call.