Analysis
In the October 2008 MTV interview, Obama was recorded saying, "I think that marriage is between a man and a woman" and that he was not in favor of gay marriage. By May 2012, he announced his support for same‑sex marriage, marking a clear reversal of his earlier position. Both the original interview and the 2012 statement are documented by reputable news outlets.
Background
During his 2008 presidential campaign, Obama held a series of interviews with MTV, where he addressed various social issues, including marriage. Over the next four years, public opinion and political dynamics shifted, leading Obama to endorse marriage equality in 2012, a stance he maintained throughout his second term.
Verdict summary
Obama did state in an October 2008 MTV interview that he believed marriage was between a man and a woman and was not in favor of gay marriage, and he publicly reversed his stance in 2012.