Unlike other websites, StackExchange does not plainly allow you to delete your own posts. Questions with upvoted answers (or something like that), cannot be deleted, for example.
This proposed site may attract very personal questions, that the OP might not want on the net in the future.
Perhaps it is a good idea to add a message before someone asks his first question. Ideally, I'd like to see something like a terms and conditions checkbox, like: "I understand that I cannot plainly delete my question." Or, perhaps it should be allowed any time to delete your own post on this site - but I'm not sure about that.
I wanted to raise this discussion before the site enters (private) beta, to have it discussed before any problems come up, that's why I've asked it now already.