Mario Draghi has claimed that the European Central Bank would withdraw its €500 highest-denomination banknote only to combat crime— not to curb the use of paper money — but you really cannot expect him to tell the truth. If he really told the truth, he would set off a panic withdraw from banks.
The USA use to print $10,000 notes in 1934. That stopped with Roosevelt and the birth of socialism to prevent people from storing cash to escape taxes. There was no excuse of terrorism or crime. Crime has actually declined. Draghi is simply engaging in political bullshit by denying the truth so he can quietly remove cash from society. Teddy Roosevelt even used recorded speeches for people to listen to during the election of 1912 to press the socialist agenda under the Progressive Party. The night of the election in 1932, there were rumors that Roosevelt would close the banks and devalue the dollar. Hoover begged him to come out and say he would not for the rumor set in motion a banking panic. Those with money withdrew it. Roosevelt came out of the high of the election and lied to the public by saying he would never do such a thing. In fact, if he told the truth, people would have poured into the banks and withdrew their deposits in gold. So he lied, and then demanded all gold be turned over to the Treasury, and then he devalued the dollar in 1934.
So never pay attention to the words of politicians or central bankers. They can never say what they will do for the public will act in a counter-trend move. Draghi is withdrawing the €500 notes for the same reason FDR stopped the Treasury from issuing high denomination notes — taxes; not crime nor terrorism. It has always been about money.