Great pictures and I’d like to point put that your hand is by the anal opening (vent would be the proper name). No joke here. That is the best place or even the tail on some species. Supporting the fish there avoids putting pressure on any of the vital organs. You could inadvertently bruise an organ or worse, cause internal bleeding. It is not likely, but when holding a fish you intend to release, you might as well take every precaution.
Even when people support a fish with their other hand, they should be mindful of the fishes spine. You could bend a fish like a U if the second hand was too far back on the fish. I saw that happen on a show this weekend. I was pretty ticked because this guy was holding a pike like that and it looked like the fish might snap in half.