Did you actually set a password 'in the program' to protect the avast program settings ?
If you didn't, you have a corrupt installation resulting it believing a password has been set and is required.
I don't have a password set in my version of avast free, so I don't know if this Reset password that you are talking about is actually in the program. Even if it were, any reset password function that I have come across, requires that you first input the old password to prevent someone else changing your password.