You made those three assumptions, you further made two more that I don’t talk to “rural” people and that I don’t know any hunters. I am not from West and a significant portion of my family lived and lives rurally, the kind that does subsistence farming in small yards with a small barn with couple of cow or sheep and a few chickens and sells a bit of produce. I spent quite a bit of time in village houses as a child and happen to live in a place that used to be more rural until urban development absorbed it, I also regularly visit places to buy produce that actually have working dogs, cats that hunt pests and have to keep firearms to kill boars and wolves. Even in such a case is hunting rarely necessary for them and while some do hunt it’s mostly to put some more food on the table for variety.

Rest of what you are saying comes back to using people killing animals as a blanket proactive justification for killing more animals for no reason. People hunting rarely for subsistence or occasionally to protect livestock does not mean killing animals in general is something to be defended as fine. Naturalistic arguments about how humans are not apart from the nature also doesn’t mean much, humans already raise and kill animals at an industrial scale and hunting isn’t more or less natural, it just is something that people do. Troubles that come with large scale animal husbandry with industrial methods of animal raising and killing doesn’t excuse killing animals for fun. Suffering does not justify further suffering. If anything, the fact that factory farming exists should exactly be reason for people to wantonly hunt animals without specific purposes. People already greatly reduced living habitat for most other animals and driving with a car into few remaining ranges to kill the animals there with gear from a hobby shop doesn’t make you a subsistence hunter.

All of that just means you like to hunt because you want to and I am going to go ahead and assume it is done so recreationally when I know many who live off the land and very rarely hunt anything as opposed to grazing a few animals and only kill boars, wolves or very rarely bears when they are within sight of their houses or grazing areas.