Why did Frodo allowed himself to be........

[Annalaliath]

And besideds if you read the books you see that Gandaf is surprised that Bilbo lasted as long as he did. So, all in all it is as such pure evil. That's the crux, the ring was evil and anyone to posses it was ultamatly corrupted by it despite their best intentions.

My advice to you, Alexandria Lumiere, is to read the books a bit more closly and to watch the movies closser too. They both have the same message about the Ring.