Same thing happened to me, my employer terminated my contract although he stated that the quality of my work was excellent. The official reason was that I forgot to add an item to the Outlook agenda. Pure BS.

At first, I was angry, confused, wanting revenge. Maybe if I'd tell the BoD about what happened, they could help me. Then I realized that this would not get me anywhere. Yes, life is unfair sometimes, but I'm absolutely certain that everybody gets what he deserves in life. The A-holes will get their share.

Then, it suddenly dawned on me. Terminating my contract is not just another problem, it's a huge opportunity. The Dalai Lama once said 'Remember that not getting what you want is sometimes a wonderful stroke of luck'. I've been working on my startup for a little over a year now, always working on it besides my full time job and family life. With the severance pay from my job I will be able to work on it full-time! Sure, money is going to be a bit tight for a while, but we'll find a way to make it work.

As far as your question goes: it's not your task to convince them they hired a lemon. It's the task of the organization to constantly evaluate their employees, including your boss.