The challenge here is that in the case of a termination a potential employer needs certain things to achieve "closure" on the incident and consider hiring you...
1. They need honesty and up-front disclosure.
2. They need you to acknowledge your errors, take responsibility, and tell them what you learned.
3. They need to believe you are a better person/pilot after the experience.
You problem is #1...if you can't give them a good, believable reason for being fired they will assume there is something you are not telling them!
If you were on probation it might be plausible that you were fired for minor clerical errors. Otherwise you need a better explanation. Worst case, tell them the reason you were given and explain that you think the real reason was personality conflict. Accept full responsibility for not being a good team player, tell what you learned about yourself and how the experience has helped you to improve your inter-personal and teamwork skills.
Under the circumstances, this explanation would be hard to contradict, sounds plausible, and is probably pretty close to the truth anyway...