All possible theories for the slip-up were subjective based on available evidence.
On June 16, 2021, U.S. President Joe Biden met Russian President Vladimir Putin for the first time since taking office. The hours-long summit in Geneva spanned several activities, including a meeting with just the two leaders and their top foreign aides, as well as solo news conferences to comment on their conversations.
While covering the American president's remarks to journalists, an event that lasted about 33 minutes, CNN reporter Kaitlan Collins posted at 1:27 p.m. (EST):
The tweet, which spread rapidly online, was an accurate description of a split-second moment during Biden's news conference.
Within the first 10 minutes of the event, he indeed referred to Putin as former President Trump, and then immediately corrected his mistake, according to PBS video recording of the news conference analyzed by Snopes. The moment unfolded like this:
I caught part of President Trump, Putin's press conference, and he talked about the need for us to be able to have some kind of ...
The moment happened so quickly that C-SPAN's transcription of Biden's remarks did not document the Trump reference, as seen here.
Nonetheless, some social media users framed the fleeting moment as an alleged "Freudian slip," or an unintentional error that revealed Biden's subconscious belief that he views Putin and Trump's political agenda as one in the same.
"They are interchangeable," someone tweeted, referring to Trump and the Russian president.
(It was true that, as commander-in-chief, Trump often spoke warmly of Putin. For instance, during their one summit, held in Helsinki, Finland, in 2018, the former American president seemingly attempted to cozy up to the Russian leader by turning his back on his own intelligence agencies, The Associated Press reported.)
However, no evidence substantiated that theory: that Biden subconsciously — or, perhaps, intentionally — confused Putin with Trump as a result of his deep-seated beliefs about them.
Additionally, while some social media posts attempted to frame the gaffe as an example of 78-year-old president's supposedly declining cognitive health, that interpretation of the above-transcribed comment was also subjective. (See here for NBC's story about Biden’s latest medical assessment, as of this writing, authored by his doctor in December 2019.)
A possible reason for the slip-up was Biden's speech impediment. He has openly discussed his stuttering over the course of his life.
Biden correctly referred to the Russian president throughout the rest of his comments to reporters, as seen in the video recording.
The news conference was part of Biden's first foreign trip since his inauguration roughly six months prior. He spent days meeting with European allies, including a gathering at NATO, the alliance formed decades ago to serve as a barricade to Russian aggression.