Assume that the overall size of the earth's crust stays the same. If one plate is pushing away from the plate next to it on one side, what must be happening at the boundary with another plate on the opposite side?
This is actually the basis for the expanding Earth theory, where some people think that new rock is being made but old rock isn't being destroyed meaning the Earth's radius is growing with time and therefore expanding! Just let me say that this is not true for a number of reasons, the lack of Earth's expanding radius not being the least of them.
But back to your question, we are a closed-system when it comes to talking about rocks, today. Overtime this wasn't the case but at this present time, we are a closed-system. This means everything we make must come from something else. If I want to create new rock then we must melt old rock.
So at a divergent plate boundary (where the plates are pushing away) plates are slowly moving and at the other end (convergent plate boundary) and they are colliding with other plates.
Two different plates such as an oceanic plate and continental plate can collide then subduction can occur. But if two continental plates collide then mountains can form. Though, subduction can still occur in this case but that explanation is for another time!