The cover story is that it will make life more difficult for terrorists and other criminals.
The truth is the ECB tested and polled to determine what justification resonated best with the public in pulling the note.
The true reason for the withdrawal of the note is that the bank wants to be able to track as many transactions as it can get away with. By limiting the number of €500 bills in circulation, even medium size transactions will require the use of some type bank-issued credit or debit card.
No cash allows the state power over your finances. Don’t like something you did or said? Freeze your bank account and you cannot buy anything or pay any bills. No cash also allows negative interest rates, another socialist idea beloved of academics.