Almost all sites will send password resets via email but without the login ID.
Your friend is correct about not sending the password IF you send the login in the same email message. The problem is you're sending both in the same email message. IMO you should just send the link to activate the account.
Then people need to click on the link and login. If they can't remember their password then they should have the option of clicking on a link so that they get an auto-generated email with a temporary password. Of course if they can't remember their login then they need to re-register and quit drinking beer.
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