Although I’m not the one you asked this question to, I’d like to give the answer a shot anyways (I did already note that I have a fondness for philosophy).
I think the simplest answer I can provide off the top of my head is: respect and obligation. Non-wild animals have been dragged into our society by us and as long as we are forcing them to be part of human society we should apply the same moral code as we do to the rest of society. They don’t have enough agency (and, in most cases we don’t know about their capacity for self-consciousness and thus their ability to rationalize which is vital in ethics) to opt out so, as long as we are opting them in it can be argued we are obligated to respect them on the same level.
I realize that “wild” animals can also show up in societies – say, a bear raiding a trash can – but if not forcibly dragged into our lives by us then we don’t have quite the same moral obligation either.
Of course, this can certainly be argued and I’ll be interested in others’ input.
On another note (and to slightly get back to the main thread), this is an excellent point and one that I think several of us were already dancing around with words like “tragic” instead of “horrible”. Sure, there’s some distasteful stuff in nature but we can accept those things as they are, in the world we have, knowing that there is no utopia (but we can still try to find respite in an imperfect world).
I actually had very much the same experience and still to this day don’t receive the same feeling in different “natural” environments. There certainly does seem to be something almost instinctual about it, but I also agree that in the end, even if it’s not ideal: