Avery
I am a doctor, not a lawyer, but if I was trying to get this enforced, I would argue that I own the right to whatever I have written, because it is my intellectual property. And when I posted it on this website, I have given implicit consent for my intellectual property to be displayed here. Now I revoke that consent and threaten to sue the website owner for copyright infringements, if my posts are not deleted.
I might or might not win, but considering that each party in the US has to pay for their own legal council, simply deleting the account and all related posts is clearly the smarter option from the position of the site owner.