The answer can be found in the science of personality typing: extroverts versus introverts. Someone with extrovert tendencies has their dopamine reward system wired to novel and fast-paced situations, while introverts tend more towards observation and internal debate before speaking. It isn't hard to see why extroverts thrive and introverts languish in brainstorming sessions, and why you could be unknowingly silencing some of the best ideas, all in the name of better collaboration.
The fix is easy. The next time you schedule a meeting, ask participants to generate a few ideas ahead of time. Appoint someone to collect everyone's ideas and then list them for discussion during the meeting. Bonus: If you want to not only positively impact your brainstorming, but also buy yourself some insurance against group think, try employing a technique on independent judgement. Prior to discussing an issue of importance, ask participants to jot down a short summary of their own position.