I'm not sure how public posts count as "private data".
Just because the data was once public doesn't mean you are allowed to embed it in a model forever.
There you'll find the arguments.
US Centric and also moot given you agree to twitters terms of service before your first post.
Says who? At best it's murky since AI companies argue that it's fair use, and that's entirely unfounded, eg. https://en.wikipedia.org/wiki/Authors_Guild,_Inc._v._Google,....