You can't prove all of them wrong because there will always be some people who dont belive in bitcoin and will call it a scam, a ponzi scheme or a bubble. That's not happening only with bitcoin, in almost all investment some people belive they are good while some people think they are scams. For example forex, I think it is a profitable investment if you are a specialist in doing this thing but a lot of people think that the odds are not in ypur favour and forex trading is something like gambling wich could be if you are a newbie and invest in everything you find.
I think a lot of people around us has told us that Bitcoin is a FAD or a SCAM or a Ponzi scheme.I don't talk about it to anyone anymore because the negativity is too much.
I am confident they will all be proven wrong in the not so distant future.No need to bother proving them about bitcoin if they don't believe it then that is OK it is their lost, If they will spread FUD then prove them they are wrong by spreading positive thoughts about bitcoin