Why I cannot select this seemingly simple edge loop?

Well, as the topic says - trying to select an edge loop around this plane but neither Alt RMB works, nor Mesh - Edges - Edges Loop.

Because it’s not an edge loop https://en.wikipedia.org/wiki/Edge_loop

Yup, not an edge loop.

Could select outer edges with alt+rmb twice, selecting non-manifold with ctrl+shift+alt+M, or in this case selecting all with A since it’s just a plane.

Can you explain me more dumbproof why an edge loop cannot be made please? The above wiki article says “Usually the last edge meets again with the first edge, thus forming a loop. The set or string of edges can for example be the outer edges of a flat surface”

If you read that Wikipedia article carefully, you will find that there are actually two definitions of the term edge loop in it: A broader and a stricter one. You quoted the broader, while Blender follows the stricter:

In a stricter sense an edge loop is defined as a set of edges where the loop follows the middle edge in every ‘four way junction’. The loop will end when it encounters another type of junction (three or five way for example).

Just accept it: This is not an edge loop by Blender’s definition. JA12 gave you tips on how to select that edges.

Thanks for clarifying. I understood how to select those “non-loop-able” edges. Now what I am trying to do is to understand the inner mechanics - if I want to make something more serious with Blender I will have work fast with the simple tasks or it will take years:-)
There is what I also found “An edge loop is terminated where the vertex has more than 4 edges (poles) or meets a non-manifold edge (an edge with only one face)” So for the edge to be able to “participate” in an edge loop it needs to border at least 2 faces? Even if only at the vertices? And if it borders only 1 face it is non-manifold?
BTW - if I understood correctly an example for “non-manifold” should be the Moebius band?

Polygonal modeling is a surface type modeling paradigm. It’s also approximation of curves and surfaces as straight edges and flat polygons are used to build those surfaces. We’re supposed to make an intelligent approximation of a form and build a surface that is enclosed, which describes a solid. The face directions, normals, are used to tell on which side of the enclosed surface the solid is.

All mesh elements (vertices, edges, faces) in a model need to be connected to exactly one such surface, and having anything else makes the geometry non-manifold. An object could have multiple mesh parts, describing multiple surfaces, but all of them need to be enclosed and the mesh elements in them only part of one.

That leaves all the possible mesh errors you can make:

  • open edges (edges with only one connected face)
  • inconsistent normals
  • loose geometry
  • edges without faces
  • connected faces describing more than one surface
  • connected vertices that are part of more than one surface

Of all of those, open edges is the most benign mesh error and widely used, as we often only need the surfaces that can be seen. When intersecting geometry, the faces that aren’t seen have no purpose and can be removed, which leaves open edges.

A model that is targeted for 3D printing can’t have that. The model needs to consist of manifold surfaces, with or without intersecting geometry. The slicing software only interprets geometry and needs to reliably determine the solid parts of the model.