Why does wave keep on travelling despite destructive interference? I've problem here. Imagine you've a line of spheres that are attached to each other with springs. You push one sphere down hard. it drags its neighbors down and which in turn pull their neighbors and so on. You have created a wave. Now you can quantify the rate this is progressing and call it velocity of wave. 
Now lets say 2 opposite waves are colliding, the sphere right in middle gets pulled down from right side and up from left. Equal opposite forces, it shouldn't move, and that's what happens. But since it hasn't moved it shouldn't pull any of its neighbors either, yet wave continues travelling through. Destructive interference didn't cancel out the wave? why.. is this model only applicable to single atoms? or something else.
Explain that please. 

rant ignore it if you want....
There is other question which was asked here and it doesn't have a suitable explanation. It just says well waves continue to travel because they have velocity.  Instead of describing the reason behind phenomena it just describes model that's used to measure it. "Why is Car moving? Well because it's going 30 mph".
 A: 
yet wave continues travelling through. 

That is one way to interpret the action you're seeing.  An alternate way to interpret it is that rather than passing through the center, each wave reaches the (immobile) center and reflects away from it.  
If you imagine a single wave pulse reaching a certain point in a medium, as neighbors start moving, they accelerate the point in consideration.  As the pulse moves forward, the neighbors ahead decelerate the point and bring it to a stop.
If you constrain the medium (such as by the end of a string being fixed to a wall), then the neighbors of that point will not be decelerated and the point will continue to vibrate.  This creates a reflected wave that travels backward.
The same situation is created when the two opposite waves meet in the center.  The opposite wave sets up forces that hold the center sphere motionless and the wave reflects.  You get the same motion on one side that you would from setting it up with that center sphere fixed in place.
A: A destructive interference does not imply that the two waves are "destroyed", it means that the sum of both waves at that point is equal to zero.
You should treat the waves as if they were two functions. Using this analogy, let us take $f_1(x)=x$ and $f_2(x)=-x$ (they are clearly not waves, they don't have a time dependence, but this will simplify the example). The addition of both functions is equal to zero at $x=0$, but that doesn't mean that the sum of those two functions sould be zero everywhere beyond the destructive interference.
