I don't think I'm a freak; can the average Joe not distinguish between the taste of Coke and Pepsi?
I've seen (uncontrolled not-scientific just-for-fun) tests where blindfolded volunteers could not tell the difference between coke and 7up / sprite.
For sure I agree with you; I think that I'd easily be able to tell the difference between pepsi and coke. But I've never tested myself.
So Coke decided to reformulate. Pepsi is sweeter than Coke, so that is what Coke did. They repeated their taste tests, got good results and told the whole world.
Where they had screwed up is that they used small containers for their latter taste tests. People are quite happy for sweetness in small quantities, but as the volume of drink gets larger they prefer less sweetness "density". Naturally the new Coke was far too sweet and there was the resultant backlash.
TL/DR: A major contributor to Coke messing up "New" Coke was using too small testing cups.