The only time to apologize for including a coworker on an email that's critical of them, is if you never intended to send the email at all. Including them on a critical email that you intended to send is actually more decent than not including them, since you're stabbing them in the front rather than the back. Apologize profusely in person and via email to everyone who received the unintended message. Keep reiterating it was an effort to vent that went wrong. Don't offer an explanation unless asked. The only response to accusations of insincerity is to repeat the apology; there's nothing else you can do. Accept criticism humbly and hope to put the discussion behind you as quickly as possible.
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