First, a small apology for the odd presentation — though it looks kind of cool, on my screen at least. I think it is kind of a pain to click on 2-image galleries to see full-size versions, but I’m not sure of another way (without a bunch of CSS) to present them similarly on the post page.
That aside, this post and the preparation of its images were inspired by a similarly-themed post I made last month. Victor from Rakmil Photography — if you are interested in learning about photography or just want to see some excellent photographs, I highly recommend making a visit — he pointed out in the comments how the medium or device of presentation affects the “optimal” orientation of an image. Most computer screens are wider than taller, so a horizontally-oriented picture will usually fit it better. My guess is this is directly related to the optics of the eye. I know I certainly favor the horizontal shot in most cases for web publishing. But…some subjects defy the comforts of the screen. I will let you be your own judge, but I think this damsel bug is one of those subjects.
Let me say, I was very happy to discover in the writing of this post that “damsel bugs” were an actual thing. Not to be confused with the damselflies of Order Odonata, these true bugs very much resemble another group of predators, the assassin bugs. Once you become familiar with the assassins, however, their damsel cousins appear a bit off. I really do prefer to have an identification for my subjects before publishing, so these shots lay dormant for quite some time because they had always stumped me.
In the above series, I have taken the same image and rotated it in the four cardinal directions. The original, how I found the bug more or less, is the one vertically-aligned with the bug pointing down. In the higher magnification shot below (uncropped), I also made a rotated version, and there I think one can see how the horizontally one does indeed “fit” the screen better. Most people probably would not notice the “upside down” orientation, but if you know the original context, I think this becomes problematic.
For these particular shots, especially the first one, I almost “prefer” both orientations. For fidelity to nature, gun to my head, I’d pick the vertical shot. Gun notwithstanding, I will leave that choice unmade and lean on the clunky WordPress image gallery.
BugPhoto.net 
Thanks for the reference, much obliged. All of this is a matter of judgement. Magazine prefer vertical for their layouts but photographers want two page spreads, WordPress does landscape best. Aome portraits can only work in portrait, hence the name.
You are very welcome, but I should thank you. Your input and insight has been very helpful to me as someone trying to get his foothold as a photographer. Cheers!