Well this is awkward.
To give him some credit, he appears to have tried.
Obama isn't the only one who makes that mistake though. @davidcameron has been heartily sitting on his Twitter handle for 6 years, despite a torrent of abuse from people who think he's the Tory leader.
In thousands of years, when the history books speak of the US/UK Cold War, it will begin with this. Then a subtweet, then eventually it will escalate into a scathing Tumblr post or a violently frank Reddit AMA.