--> Nothing wrong that coworkers want to perform and every boss wants to see it - you can get used to it and be more competitive. Next time, you will reply the email to everyone that you will take care of it if you believe you are the right person to handle it.
同意你的所有comments, 但是，具体这件TASK分两个连起来的部分，第一部分是我做的，如果你不知道这个部分，不知道整个PICTURE,你是没有办法做第二部分的。问题是，这个同事想当然的自己做了第二部分，结果完全是错的。
--> The resaons behind it could be various which could be totally out of your control and your boss doesn't have to explain everything to you. Your boss has his power to make it the way you wanted but he might have his concerns or his ways to handle things. Or, maybe, at least, he was happy about the fact that someone stepped up to help even though it didn't work out well.
从我的了解来看，你最后的一个情况，就是这里的情况。
听起来，你有做BOSS的经验。Please take a look at my anwers in my other follow-ups.
Thanks for sharing.
