Most young boys and teens I have talked to that wanted to hunt and didn't hunt had one simple reason. Dad was not around to teach them.
There are a lot of reasons, lots of them Chad covered. But mean words are not likely one of the reasons.
Anti hunters come in several forms.
The ones that are really just apathetic and ignorant of what actually happens. Those you might be able to get too. Mainly because they don't like what they don't know. And some education might help.
The ones that don't like it because of the hunter/hunting stereotypes. Those are a bit harder to reach but maybe not impossible. Still, I'll use whatever words that come to mind to make my point. Might be field dress, might be gut. Might be process, might be butcher. Might be finish it off, might be cut it's throat. I make my arguments in reality, and the reality can be pretty rough.
The militant anti hunter. Piss on them. They don't feel any different about us either. Those folks you have to fight. There is no reason. No more interest in change than Brady or Feinstein.
My daughters went to the 4H Fur, fish, and game weekend. The youngest went through Hunter Education that week. But for both weeks the wardens brought in a deer and processed it right there in front to them, start to finish. Then they ate it the next day. At some point you have to make the mental jump to the reality that hunting is a dirty business if you are successful. And things don't always go the way you want.
BTW, if we are going to talk about negative connotations and stereotypes were did you get the idea it was a small caliber? The entrance wound won't tell you that. Heck, the exit wound might not either if it does not expand. Did you just assume the young lady shot it with too small a rifle? Maybe. But IMO assuming you know it's a small caliber because it was a teenage girl is up there with blaming this for liberals hating hunting. Not exactly promoting a welcoming environment for that young lady are you?