Besides the technical considerations others have posted: who exactly owns what you post? If you send a letter to someone, is it you or the receiver who owns the letter? If you post something publicly, is it you or the collective public that owns that post now?
Thinking about this via copyright is not very helpful as small text are rarely complex enough to fall under copyright. However most large social media force you to sign over the copyright of anything you post to them anyways.
And the law IANAL does not consider public texts to be "personal data". This is reserved to you real name, address, email, IP etc. Stuff that can be used to identify you, but not more.