The reason it's so widely believed is not because of the empirical evidence but because it coheres with Neo-Darwinian theory. If naturalistic evolution is true, and all naturalists and many non-naturalists believe it is, then humans simply must've arisen from some earlier primate species.
Now, we may have, of course, but the empirical evidence, other than general anatomical similarity, doesn't warrant the conclusion that we did.
The following 8:00 minute video, the eighth in the current Science Uprising series, discusses why the fossil evidence that exists falls well short of being conclusive. Indeed, the fossils that have been unearthed have turned out to be those of either human beings or apes. There appear to be no definite intermediates.
An idiosyncrasy of the series is that the narrators wear Guy Fawkes masks. David Klinghoffer at Evolution News explains; the symbolism behind it:
The mask is a reference to the 2005 film V for Vendetta, inspired in turn by the historical English rebel Guy Fawkes, and a comic by David Lloyd, who is right when he says it has become “an icon of popular culture,” “a common brand and a convenient placard to use in protest against tyranny.”Here's the video:
The symbolism of masks has evolved in the meantime, but the tyranny of scientism has remained a constant, or in fact grown more perverse and obnoxious, making the series of short videos more relevant than ever.