Because time is considered to be the independent variable, with distance being dependent on the time elapsed since some starting point.
Also, distance can be treated as function of time but time will not be a function of distance unless the object is always moving away from the initial position. If the object is stationary or returning, the distance-to-time relationship becomes one-to-many which is not permitted for a function.
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The speed is the slope of the curve in such a graph.
distance time graph is a graph traveled in a graph which shows how much we have traveled in equal period of time.
The slope of a distance-time graph represents speed.
Typically distance is plotted on the y-axis of a distance-time graph.
speed is the gradient under the distance vs time graph which is change in distance /change in time