Hi Sivatorne.
What you're experiencing is definitely worth exploring because, as you suggested, having a hard time working with a team to reason things out could affect your business school success and success in other areas of life that involve working with teams on projects.
Part of the answer is that practice makes perfect. So, in a way, it's fortunate that you have been studying for the GMAT with other people since, in doing so, you have become aware of this issue and also have an opportunity to practice improving your skills in this area.
Regarding what could be tripping you up, factors that often are at play in such situations are play are fear, anger, and lack of confidence. Also, you may have some misconceptions about how to best communicate your ideas.
One way you could seek to address the issues is to mention them to the people with whom you're studying and get a little help from them with sorting out what you're doing. A lot of the time, the reason we have a hard time working with a team is that we're overemphasizing going it on our own. So, by enlisting your teammates to help you, you may begin to solve the problem.