If we are flying at high altitude say 6000ft and want to climb to 7000ft why do we need to maintain Vy and not Vx?!
As others have said, you wouldn't normally use one or the other for such a climb.
However let's imagine that your only two choices are Vx and Vy.
Vy will result in you having a faster forward speed than Vx(so get to your destination faster than Vx), and have a faster climb rate than Vx (so got to the desired altitude quicker than Vx).
So to turn your question back at you, why would you ever choose to use Vx unless you needed to clear an object in a given distance (not time) which wouldn't be cleared by using Vy?
I hope that helps to answer your question.