Why are the axes in Minkowski diagrams swapped when comparing with diagrams in classical kinematics? In diagrams in classical kinematics, the time coordinate $t$ is drawn horizontally and the spatial coordinate $x$ is drawn vertically.
Why are Minkowski diagrams drawn the other way round?
In classical kinematics, we like to picture position as a function of time, so having time on the horizontal axis in a diagram simply corresponds to the usual way we draw the graph of a function.
I get that in relativity, position and time are on equal footing, so that the functional aspect may be deemphasized. But since it is a pretty big hurdle to compare relativistic kinematics to classical kinematics if we always have to flip the diagrams in our heads, I would expect that this would be only done if there are some striking advantages. However, I couldn't think of any.
What's even more strange is that we still write vectors as $(ct,x)$ instead of $(x, ct)$. So we are also making it harder to apply visual intuitions based on the usual conventions in linear algebra (like picturing the action of a familiar matrix on a vector). Maybe the conventions in linear algebra are actually more recent than the conventions of special relativity.
edit: Although the other question has an accepted answer, it does not answer the question of why the convention from classical kinematics was discontinued. It simply reiterates that it is a convention (and a comment expands that this convention can be traced at least to a 1909 paper by Minkowski himself).
 A: It's mainly a matter of aesthetics, and it's more natural (at least in my opinion). A special relativity course typically starts with a Gedankenexperiment involving two observers moving with respect to each other; the canonical example is that of a moving train and a platform. The reference frames of these observers can be drawn like this

where the direction of motion is along the $x$-axis. From this, it's fairly straightforward to then represent both reference frames in a single spacetime diagram, where the $x$-axis remains horizontal. One can also keep the $y$-axis, so that the spacial coordinates in the rest frame lie in horizontal planes of equal time. In addition, light-cones are vertical. I'd argue that this looks better than vertical space axes and horizontal light cones.

It also highlights a conceptual difference with classical mechanics. In the latter, time is agreed upon by all observers, so it makes sense to write a path as a function $x(t)$, i.e.  time is a parameter. In special relativity however, the flow of time depends on the reference frame, and time gets upgraded to an additional coordinate, placed on the same footing as the spatial coordinates. A path is therefore more conveniently written as a parametrized curve of the form $(t(\lambda), x(\lambda))$. In other words, a spacetime diagram is a depiction of a coordinate space, rather than the graph of functions.
Regarding the convention $(ct,x,y,z)$, this is not universal. I've seen textbooks where $(x,y,z,ct)$ is used. But $(ct,x,y,z)$ is more convenient, because it's often rewritten as $(x^0,x^1,x^2,x^3)$, and physicists regularly switch between both notations.
Are these big hurdles for students? I don't think so, compared with more abstract representations like phase-space diagrams or general coordinate transformations. In any case, it is important for students to learn that visual diagrams are a tool, and that different problems often suggest different tools. Likewise, students should become comfortable with switching between different notational conventions. Learning physics is all about expanding your toolbox.
