When I was in school, I liked working alone. I hated group work because I generally felt like I was going to work harder and smarter than my teammates and I didn't think they deserved to get credit for my work. I also usually felt like group assignments were not so big that I couldn't just do all of it myself.
I think in my adult life (both personal and professional) I've come to appreciate different times when group work vs. independent work can actually be beneficial. First of all, it is very rare in most professions that you will be working completely independently. Also, the "real world" does, on occasion, mimic the school environment where some people naturally over-achieve and others tend to allow it. It is good to prepare yourself in advance.
On the other hand, in professional environments, a few benefits to group work is that you often get to choose the people with whom you will work. This makes a world of difference. Also, the projects that require groups to achieve the goal really are big enough that one person would be swamped to do it alone. When there is a common goal, and group members know their own strengths and weaknesses (which only comes with group-work practice), typically working in groups functions far better than working independently.
As a teacher, I am much better at facilitating group work knowing what I do from real world experience. With the right guidelines, and the right kind of projects, group work really can be beneficial for everyone involved.
On the other hand, I am still sympathetic toward those students who, like me, prefer to do everything themselves. I cannot help but know exactly how they feel.