Hi @Zoltan, welcome to the Asana Community Forum! 
When you merge your Asana accounts, you will be asked to verify your identity by re-authenticating your primary Asana account. This means that you will have to re-login with the existing email address in order to add a new one. You need to add the password of the Asana account you are currently logged in, not the password of the account you are merging in to this account.
I hope this helps! If the issue persists, I recommend you to contact our support team so they can investigate the issue further: How to contact our Support Team ✉