As I said in a comment, I think that "How can I persuade people that I'm right and they're wrong" questions should be off-topic, regardless of the opinion.
Your edit in its current form is much closer to an IPS question, but I still would not have voted to re-open. The question, shorn of rantiness, that you have boiled down is
How can I tell [my mother], and anyone else I see doing it, that it's upsetting for me to see them kill these creatures?
The trouble with this question is that without more context, the answer is going to be essentially
You say "it's upsetting for me to see you kill these creatures."
That's not particularly helpful, because we don't have any context about whether the OP has already tried that approach, what else they might have tried, what the response has been to whatever they've attempted, or what their goals might be besides stopping the ant-killing. For example:
- Is being heard and understood enough, or does the hearer need to make some concession for the OP to feel satisfied?
- How significant does the concession need to be? Would it be OK if Mom waits until the OP has left the room to deal with the ants, or is that still horribly upsetting?
- Would it be enough if Mom agrees to work hard to avoid attracting ants to the kitchen?
- How important is it to the OP to preserve the interpersonal relationship, relative to the importance of stopping the insect killing?
- Besides Mom in the kitchen, does the OP also want/need to have this conversation with their teacher/boss/friends/coworkers? What about strangers on the street who aren't watching out for ants when they walk?
And so forth. Without this kind of information, answers are likely to be either very general, incredibly long in order to allow for all the various possibilities, or else hit-or-miss in terms of how helpful they are to the OP.
Having said all that, it seems that many questions here leave out what I would consider important context of this sort*, and I have pretty much given up on expecting it, so I'm not going to VTC now that it's been reopened.
*How to tell people I'm not their tech support? is a recent example of a question that does a very good job of including this kind of context. There's some factual background, and then an enumerated list of goals:
My targets are these:
1. Tell those people, who expect me to help them with their totally random problems, that I'm not their personal technical support for their printer or whatever
2. Do 1) without hurting their feelings a lot, I'd rather tell them that I'm just not competent enough to fix their problems, however, this is not an option due to my field of study. (Note: I already tried this and it was ignored, because "I know that, because I study computer science")
3. Still have them feel like I'm a helpful person, but not a magician