This note by Ezra Klein on the political implications of false beliefs about income/class mobility is particularly on point:
It turns out that there's a bit of a paradoxical relationship between believing your country has a lot of economic mobility and your country actually having a lot of economic mobility. If you believe that your country is extremely mobile, you're likely to believe the results of the economic competition are relatively fair. As such, you won't want to slap the rich with particularly high tax rates and you won't be terribly concerned about spreading economic opportunity. After all, anyone can make it!
On the other hand, if you don't believe your country is terribly mobile, then you're less likely to believe economic outcomes are fair. And if you don't believe the outcomes are fair, you're likely to tax the winners relatively heavily and plow those profits into things like universal health care and free college. Policies, in other words, that spread opportunity more widely and thus make your society more mobile. Put like that, it sort of makes sense. If you believe your society is already economically mobile, you don't spend a lot of time trying to solve the problem of insufficient economic mobility. if you don't believe that, then you implement policies meant to increase mobility.
Click on over and read the whole note, including graphs from a recent Brookings Institution report on just how deluded Amercians' beliefs are.