The new Amazing Spiderman is just a typical boy who's sort of selfish. The movie tries to push for a new motto of "Know who you are," which, to me is just euphemism for "What's best for you is what's best for everybody.". It's fair, but there's nothing heroic about that, at the heart level. Superheroes are suppose to inspire us to become the best we can be, e.g., when we choose altruism in a situation, we are partaking in Spiderman's greatness in a small way, and that makes us proud and happy (besides the noble gesture itself). And when we choose to exercise our God given talents for the sake of the greater good, we are conceding to the notion that "With great power comes with great responsibilities.".
Now, in what ways has this new Spiderman acted in the interests of the public good, looking beyond himself? He hasn't...
1) Sneaking around Oscorp would get Gwen into trouble, but he didn't care.
2) He was suppose to pick up Aunt May, who has loved him and raised him, but instead he stayed with the doctor, who neglected him all his life, even though he was his father's long time colleague.
3) His superhero works were merely the byproduct of him trying to find Uncle Ben's killer, and he does that only because he felt guilty.
4) He fights the lizardman only because he felt bad about being the one responsible for creating him.
5) He snuck into Gwen's bedroom and coaxed her.
6) He broke his promise to Gwen's dad on not getting Gwen involved anymore, knowing that it would put her life in danger.
The movie even has an anti-heroism theme. For example, consider the way Uncle Ben died. He could have left the robber alone (and he absolutely should have, the movie was trying make acts of heroism look really stupid). The whole incident just screams "Don't try to be a