The space and time axes are separated to emphasize that time has no direction in space and vice versa.
They are still both horizontal (and consequently parallel to each other) only to fit 3 axes on a 2D display and maintain the step-by-step progressional synchronization between them.
There are other (arguably better) schemes to depict the same relationships on a 2D display but I will stick with this one for now because it was the first one mentioned.
Anyway, that graph represents an infinite numerical series that can be written in the differential form that states how much each aspect of motion has grown or shrunk, compared to the previous unit in the progression. This series can be written like this:
+1Δs/+1Δt, -1Δs/+1Δt, +1Δs/+1Δt, -1Δs/+1Δt, +1Δs/+1Δt, -1Δs/+1Δt, +1Δs/+1Δt, -1Δs/+1Δt, +1Δs/+1Δt, -1Δs/+1Δt, ...
...or this series can be written in an absolute form ( where the numbers denote the absolute magnitude of space and time, as measured from the ORIGIN OF THE RELEVANT AXIS - marked in red color ) which can be written like this:
0s/0t, 1s/1t, 0s/2t, 1s/3t, 0s/4t, 1s/5t, 0s/6t, 1s/7t, 0s/8t, 1s/9t, 0s/10t, ...
Obviously we can transform the differential form into the absolute form by integrating it.
Now, that we have the basics behind us, we must ask ourselves:
"How can we be certain of the signs appearing in the numerators or denominators of the differential form ? "
The intuitive answer is that we can simply see it on the graph.
For example, we might assume that for the spatial aspect, an arrow pointing left means + (a positive, outward "direction" or growth of space) and an arrow pointing right means - (a negative, inward "direction" or shrinkage of space) and for time - vice versa, but that is only a feature of the graph.
But that answer is wrong in the context of RST because it relies on the directional relation of these arrows to the white background of the graph !!!
In RST there is no "white background" that a "direction" can be related to. The only relations are between motions (units of motions), and the "white background" does not represent any motion !
Do you see the inherent problem in such graphical representations of scalar motion in RST?