If he becomes the antiChrist he may want this idea to at least be out there to help promote him as the savior of the world. The mystery about his father would definitely help on this account.
He would only become aC if he is booted from here and takes up residency somewhere in what use to be the old Roman empire, possibly Syria. If this happens it would not surprise me as he seems awfully "antiChristy" but it yet could be another.
Maybe he is a trial run experiment but as long as Christians, as a force that The Holy Spirit moves through to constrain evil, are still here and haven't yet been raptured (something that they also may contribute to aliens) the aC cannot prosper.
Maybe the Rapture HAS occurred....and only one or two were worthy, so no one noticed it!