Why does Gene agree to forego his studies and venture to the tree?

Gene forgoes his studies and agrees to venture to the tree purely because Finny advised him to continue with his studies if that's what he felt he needed to do. He agreed because he wanted to defy or be in opposition to Finny, it's that simple. To get a clearer understanding, think about a time you did something just because someone told you not to, not necessarily because you wanted to, but rather because someone else told you no.