why does gene try to blame finny for saving his life

He says that if it wasn't for Finny he wouldn·t have been on the tree in the first place.

Here is a more detailed response from GradeSaver,

The beginning of Chapter 3 is a great contrast with the ending of Chapter 2 in terms of both tone and sentiment. At the end of Chapter 2, Gene says that he was grateful to Finny for keeping him from falling out of the tree; but, at the start of the next chapter, he accuses Finny of being responsible for the whole thing, and owes his friend no thanks, since Finny is the one who goaded him to go up there in the first place. Gene is rationalizing away his feelings on the near accident; unlike Finny, Gene shows difficulty in expressing or even admitting emotions to himself, as displayed by this change of heart. The statement also demonstrates how Gene's nature is tainted by his jealousy and negative feelings for Finny, which corrupt his behavior and his good nature.