Let's take a brief look at the history.
Spanish Inquisition's goal was to suppress heresy - or, in other words, preserve traditional religious beliefs. It was a conservative movement that resulted in executions of thousands of people.
US itself was founded by progressives - conservatives were known as Loyalists at the time.
Over the last couple hundred years conservatives, standing athwart history (in the words of William Buckley), have opposed most of the civilization advances that we now take for granted:
- emancipation of slaves
- women's suffrage
- 8 hour workday
- limitations on child labour
- desegregation and racial equality
- Social Security
And you don't have to go too far back in time - it is probably safe to say that in 1960s most conservatives supported segregation, and that in 1920s most of them were against women's suffrage. You just cannot say the same about liberals.
Today, history is repeating itself with conservative attitudes towards everything from torture and gay rights to healthcare reform.
So why is the conservative brand still acceptable in the mainstream society after all of this? What am I missing?