First, let me explain the term "space" as used here. Space is really an empty void, a vacuum, nothing. So what is meant by "space" here is the "metric" of space, which can be visualized as 3-dimentional grid lines overlaying space. This is what can change, not real space. Secondly, the speed of light is CONSTANT (always the same) in a vacuum (space). Speed is distance / time (in this context, distance is measured on the grid lines).
Since mass causes spacetime to change (Einstein's General Theory of Relativity), the reason that both "space" and time have to change together is because the speed of light is a CONSTANT. Speed is distance / time (in this context, distance is measured on the grid lines, or in Einstein's equation in his General Theory of Relativity, spacetime curves in 4 dimensions).