|In many instances, the word "eccentric" is a codeword for weird or difficult, while being "very sensitive to criticism" is often a code-phrase for being defensive, insecure, and temperamental. Nonetheless, now that you and your co-worker have crossed paths on the same project, both of you should meet with your manager. |
His rationale for giving you the same assignment could be based on his desire to see how both of you approach it, or perhaps he wants two independent views of the same issue. At the same time, this type of assignment could also be a sign of his incompetence or confusion. The only way to determine your next step on the assignment is to sit down with him.
The fact that your manager is sensitive to criticism is not a problem in this instance, since you are not going to criticize him. Rather, the two of you should let him know about the overlap and ask if he wants you to continue to work separately or in collaboration from this point. His response is likely to give you some insight into this project and into this manager.