Your comment on Obama's error isn't quite correct. It was Chief Justice Roberts who mangled the words and Obama followed suit. The look on Obama's face was priceless at the moment he realized that Robert’s had erred. Before his entry into politics, Obama was a lecturer in constitutional law at the University of Chicago Law School. Since the form of oath is a Constitutional requirement he retook it with the correct wording afterwards. https://www.theguardian.com/world/2009/jan/23/barack-obama-oa
https://www.theguardian.com/world/2009/jan/23/barack-obama-oa