I like the analogy so let me continue it further - If "you" (the person in the quote not you Jono8) ban the dog poop from "your" table, does the dog poop idea just go away? No, it just moves to other smaller tables and yet because "you" can't see it any more "you" feel happy that it's gone and think "you've" done something good and the dog poop on table idea must have gone away.
Only you haven't, because now the dog poop on a table idea is still spreading across more tables only now there is no-one to tell people about how bad it is and try to change people minds on why dog poop is bad so the tables get bigger and the dog poop idea gets exposed to more people and, whats worse, is that while the "dog poop on tables" movement continues to grow "you" have no idea that it's happening because "it's not happening on my table" so "you" still think "you" did a good job and are praising "yourself" whilst being blind to the huge increase of dog poop on table believers.
I would suggest that is a more accurate and "full" story rather than the quoted image which, for me at least, stopped at "I banned it so it all must have gone away" which I find to be the response of an immature mind, a bit like sticking your fingers in your ears and believing that it you can't hear it then it doesn't exist, rather than facing the reality that these ideas need to be heard so that everyone can point out why its a bad idea using calm rational facts and humiliation as the number of the dog poop fans slowly dwindles. They'll never be fully gone, real life doesn't work that way, but you can keep the numbers really low and prevent new people thinking that way using those two tactics.
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This is basic human psychology - if your belief is "attacked" it gets stronger. If others see you being attacked over your beliefs, and they are sympathetic to you, their beliefs will get stronger too. However if you calmly and rationally talk to people you have a far better chance of changing that persons mind than if you "attack" their beliefs. It's not 100% guaranteed that even calm rational discussion will change everyone's beliefs, but it's a damn sight more effective than screaming in their face and banning them is.
For example,
I love the work that Daryl Davis does. He's a black man who goes to KKK and Neo-Nazi meetings to talk to people, not attacking their beliefs but listening and calmly, rationally talking to them,
and he's de-radicalised hundreds of Clan and Nazi members. Compare that to how many have been de-radicalised just because they've been banned from twitter, and where they now feel attacked by twitters "hatemobs" which hardened their beliefs? Worse still no-one can talk to them any more to try to de-radicalise them whilst those on Twitter feel "happy" because they got that racist off their platform even though they've made the racist even harder to de-radicalise - how is that a "victory"?
As I mentioned earlier, I think it's reasoning of an immature mind, where the "hear no evil, see no evil" path of "If I can't see it then it's not happening and if it's not happening then I'm happy" eventually leads to trouble, because it hasn't gone, it's only got worse and now it's harder to fight while they Twitter mob feel happy, clapping each other on their digital backs but blinded to reality.
But again that just my opinion. I know which I think changes more minds