Do Pets Mimic their Owners?

Or is it just a coincidence that they start to take on our traits? Maybe the environment makes them the way they are and since we're sharing environments...

I just wonder because my bird is very nervous, moody and is slow to trust anyone. In other words, he's a lot like me. I wonder if it's because he is faced with the same situations as me or because he watches how I react to things and senses it and tries to mimic the correct behavior. It's food for thought. I feel bad though. I don't want him to be like me. He deserves better than that!