The first theme is hinged on the value of identity. Identity was emphasized throughout the movie, whether it was hiding it or manifesting it.
At the beginning of the movie, it is all about the Incredibles hiding their own identity. They have to live discreetly in an unassuming abode after a series of lawsuits directed at Bob. According to the law, they have to change their identity and live amongst ordinary citizens. They have to maintain a low profile, and live just like any ordinary family, with Helen being a normal housewife and Bob being an insurance agent, without eschewing the harsh reality of being reprimanded by the querulous manager all the time.
Although having to lay low, Bob's desire to act like a hero has never been aborted. He often tries to save people when he can, but activating their superpowers is treated like an aggression. He nearly got arrested by the police when he is trying to save people from a fire.
Apart from Bob and Helen, the children of them cannot say who they really are too. This is seen when Helen gives the eye-shield to Violet outside the cave on the island, telling her "Wear this, identity is your most valuable possession." Also, Dash cannot run at school's sports day, because he cannot let others know he was a 'superboy'.
Yet, towards the end of the movie, when the citizens of New York City start to appreciate how the Incredibles help them to fight and destroy the giant robot, they are not afraid anymore to admit who they really are. The meaning of "identity as their most valuable possession" is slightly twisted comparing with the beginning. Identity is so valuable to them that they are only too proud of it to hide it again.