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I've only read half of the letters (9 of 18 pages) so I apologize if I'm missing the point, but why didn't Cary suggest that the LW speak with his neighbors about their cat? And if he doesn't know which neighbor it is who owns cat, perhaps he should ask around.
You folks have been taking the LW to task for insensitivity to animals, but how about insensitivity to humans? How would the LW's kids feel if someone killed their pet? And more in his self-interest, what if he someday needs a favor from his neighbor? Even if he manages to kill the cat without the neighbor finding out what happen, he's likely to fall under suspicion unless his neighbors are as xenophobic as he is.
It's so sad when people are afraid to emerge from their own houses and just talk to the folks who live only a few yards away from them. I think the LW has real problems.