So the two party system hoax, is bore out but an illusion that does lend to this thinking, and it can be understood why.
In FPTP voting systems there is a strong tendency for each election for there to be at most 2 parties that collect most of the votes. What a FPTP system does not do is cause the same 2 parties to consistently win during each election.
But its an illusion because it is not reflection actually support from the people. They will vote for someone other than who they want as a compromise. Sot eh actual "real" support is usually wildly different than the public manifestation of support in the form of votes.
In other words if parties have A: 35% B: 33% C:32% in terms of peoples preferred candidate, what you will see is the actual vote will turn out to be A:51% B: 49% C: 2%
However the very next year if C gains 1% support and B looses 1% support then the very next year you will see a sudden shift in votes at A: 51% B: 2% C: 49%
So while there isnt **really** a two party system this illusion tends to make people thing it is. Then once they think it is it becomes self reinforcing people people are idiots.