Ok, now I’m not a linguist and also not English, but in my opinion there’s a difference. “People” is a broad undefined group. “Persons” is a more defined group.

Adding “those” in front also alienates them further. So by saying “those people”, you are distancing yourself from them, despite then being your family. That is the amusing part for the person you talked to. You mildly insulted your family.

In a similar vain, “some people say” all the stuff that you won’t to be heard saying yourself, even if it’s your own opinion.

Or in some places (this might be more local) using “you” instead of “me” when answering personal questions. For instance if someone asks: “How does it make you feel?” and answered: “It makes you feel sad” then the person answering it is distancing themselves from their own answer by literally answering on behalf on some unknown “you” when they should be using “me”. Using “people” is sort of the same just on behalf of someone else.