The comments are an eye opening experience, amazed to see how so many people think they don't have a huge responsibility to the owner of personal information. More of a reason why GDPR is needed.
While you may be amazed, this is literally now the truth in EU.
The right to control such information is established as a right of the individual; and if you have possession of some information about me, then yes, I have more rights to control what you are allowed to do with this information in your hands than you, and that information can never in any way fully become "your property".
As if possessing something makes it your property - property is a legal notion and (in democratic countries) means just what people want it to be.
Devils advocate -- if I write a poem for instance, and post it online, then copyright law still gives me control over uses of that information. People don't have the right to do whatever they want with that info. Is this so different?
Similarly, companies often include EULA and shrinkwrap contracts governing what users are allowed to do with information accessed on their webpages. So why can't users collectively write a similar contract pointing the other way?