Leftists believe this because they expect and allow their leaders tell to them what to think, read, watch etc., and they think everyone does. They cannot imagine that there are people who actually decide such things and think for themselves.
The Leftist pawns cannot comprehend the extent of their own self-mockery, i.e. that they believe themselves to be liberal but are in fact closed minded, to be tolerant but are intolerant, that they love diversity but in fact demand conformity, that they are sophisticated though in fact they are sophomoric, that they are above and ahead of everyone else whereas the opposite is true, that they are wise but in fact are stupid.
Truth is scorned by the Left, though the Leftist pawns cannot understand this and are themselves blinded by self-deception.
They tend to think that everyone is like themselves, but this is just another effect of self-deception and lack of sophistication.
:psychological projection does seems to be the overwhelmingly favorite “progressive”s hobby doesnt it