What’s it called when you make a statement, but find one example of something that goes against it, but your statement is still valid? (example: you say “nobody in this town likes cats,” but one person out of thousands likes cats. you’re statement is still true, you just found an outlier)

You should be talking about a Rebuttal which is a refutation or contradiction to your own information. Which is used in a persuasive or formal essay to make your argument more solid, and concrete. 

Here is a link if you need more information.
http://education.seattlepi.com/write-rebuttal-essay-2130.html

Hope this helps! Please let me know if I am right or wrong

Holy place could be one