The way I think about it, it’s not the specific numerical values in the static filter that reveal its properties. Instead, it’s the symmetry (or lack thereof). In the quiz example you provide, there is a symmetry around the horizontal axis…impact of the filter is the same above and below its center. However, it is not symmetrical around the vertical axis…values from combining the filter with the input signal are pushed in opposite directions. So in this case, any differences between the left and right will be enhanced. In other words, a vertical edge.
Notice that this is consistent with your text description of what you were taught.
The example has both 1 and -1 (and 3 and -3) both above and below the center, it’s symmetric, so horizontal edge is not correct.
It’s not the numeric values 1 and -1 themselves that are the clue, it is the way the weights are distributed throughout the filter. Hope this helps