There is no "your family tree" or "my family teee". There is only "our" one big world-wide family tree and we all contribute our family twigs and branches to the tree. Because other people connect their twigs to the WikiTree branches, the profiles need to be open or public so that everyone can see where to attach.
An individual "leaf" for a living relative can be further privacy protected as needed.
If the one big WikiTree seems like a good fit for your needs, we hope you will join us!