As beautiful a character as Phineas is, he fails to understand the world in which he lives. Gene's reaction to Phineas openly expressing admiration for Gene demonstrates this:
"It was a courageous thing to say. Exposing a sincere emotion nakedly like that at the Devon School was the next thing to suicide."
Phineas is living amongst young men who are focused on both machismo and heirarchy. To be sentimental is to be an outcast and to lose power in the heirarchy.
It is lack of understanding about the inherent heirarchy in social settings that leads to his other moments of naivety. Phineas can not see that the boys are in competition, always. He fails to understand that Gene studies, because he knows Gene is generally better at school than he is - so why would Gene study?
"I didn't know you needed to study," he said simply. "I didn't think you ever did. I thought it came to you."
He doesn't understand that Gene is trying to push higher than the other boys, and so also doesn't understand that Gene sees him [Phineas] as a threat as well.
It is this last piece of ignorance that is so dangerous, as it inadvertenly leads to Phineas' injury.