Long answer: When you try to do destructive interference, you do it only in specific places, you have valleys and peaks somewhere else. Energy from valleys (detructive interference) just enlarges peaks and makes them brighter. As first commenter on that topic said, you can't make destructive interference without making constructive one in different place, so energy is not lost.
Turns out if you only use first few frequencies of FFT the filter output will look like it respond slightly before the signal arrives. It's a freaking time machine.
There are filters with negative group delay, however. But FFT is irrelevant for that and it's not a time machine either.
A bit harder to realize with electronics or mechanics than software though...