The title of this makes me annoyed. What parity? They're both abstract made up units that happened to be even on a random scale for a while. This is financial numerology :-( (yes, I know there's more content and "this week's currency summary" sounds less fun and I should chill out)
Parity can just mean equal. And the Euro’s creators clearly targeted a value similar to the dollar.
Exchange rate was 1 EUR for 1,95583 DM