There are three combatants in this war of the words, and each has contributed to the present battle. Right from the outset, none of this belonged in an email message. Email can be excellent for conveying facts, figures, and straightforward information. However, when it comes to reprimands, personal matters, disagreements, or emotionally-charged exchanges, email should not be the channel of choice.
If your co-worker did a singularly horrible job on his side of the project, you are within your rights to provide some feedback. The best way to do so is in person if possible, or at least by telephone. The objective of this communication should focus more on finding solutions than finding fault.
When receiving an email message such as yours, it could easily be argued that your co-worker should have contacted you to discuss it. Instead, he ran to your manager, either in person or online.
Upon reading the email you sent to your co-worker, your manager should have met with you or called you to discuss not only your message, but also your co-worker's performance. Instead, in an act of corporate irony, he sent you a scathing email that chastised you for sending a scathing email.
In the future, the best way to face this type of situation is face-to-face.
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