"I don't see why the current generation needs to pay for the previous generations fairytale promises."
I'm afraid that is exactly the way the UK State pension sytem has always been run - the cash paid in today by the workers is used to pay for the current pensioners
it would have been better if in 1913 they had set up a proper allocated pot sytem but it would have been 30 years before any pensioner had accumulated enough to live on
as they needed to do something straight away (and they needed the votes of course) they went for a current funding model
theoretically this has some advantages - you don't have to invest the cash for 30 years and you can quickly change the pension payments (in & out) if things get good or tough