I think it's the movies fault to a big extent. I watched the movies first and didn't like Frodo at all. But then I read the books and I was surprised at how much PJ ruined his character. These are character building moments for him, look what PJ did to them:
1) His actions on Barrow Downs. He resisted the urge to put the rings on, called for Tom Bombadil and saved everybody. --> Deleted on movies
2) On Wether Tops, he calls the name Elbreit, which makes the riders scared. And he even tries to stab the Witch King, which they find a piece of his clothes later. It means he could have stabbed him with the same blade that Merry later uses on him. --> in movies he just screams and falls down on the ground.
3) He stands up and calls the ring wraiths to attack him in Rivendell. --> Replaced by Arwen in the movies.
4) Sam thinks he is just gullible to trust Gollum in the Black Gates of Mordor. But then Frodo tells Gollum I know exactly what you're looking for so I have to make you swear to the ring. Sam realizes he was wrong about Frodo, he is just that good of a person to be kind to Gollum. --> In the movies he is actually gullible and does trust Gollum. The swearing exist, but it doesn't effect anything.
5) When they meet Faramir, he speaks with intelligence, in the way that Faramir is impressed. Sam tries to join in and says something stupid, and Faramir asks him to let Frodo do the talking since he doesn't know how to. It shows once again, his wisdom. --> In the movies he is useless in convincing Faramir, and it's actually Sam who get some senses into him with "Do you know why your brother died" speech. Again, even in intelligence and wisdom Sam is superior to him in the movies.
6) When Witch King is marching to attack Minas Tirith, he senses something and tries to make Frodo put the ring on. Frodo battles it and stops it pretty easily. --> In the movies he acts like a mad man and Sam and Gollum have to forcibly stop him from putting the ring on.
6) Before they go into Shelob's lair, he is on good terms with Sam and when Gollum sees him sleeping on the stairs he almost stop his plans. Sam shouts at Gollum and ruins it. --> In the movies Frodo thinks Sam ate the bread and asks him to leave and gets into the lair. Proves once more that he is gullible and stupid.
7) In mount Doom, Gollum attacks Frodo and Frodo curses him based on that oath he took before. When Gollum attacks him and bit his finger off, the curse of the ring works and he falls down. so Frodo basically did destroy the ring, but indirectly. --> In the movies Gollum just says "Smeagol lied" and attacks with no problem. Frodo attacks to take the ring and they fall together. It's still the same concept and Frodo destroys the ring indirectly, but the oath becomes worthless and furthermore proves his stupidity.
8) Frodo acts bad toward Sam only twice in the books, and that was the two times that Sam asks to carry the ring. Other than that he's always kind towards him. He also can put the ring on, it wouldn't GPS activate his location, but fights the urge because Gandolf told him not to. --> In the movies he's a bitch to Sam every 2 seconds "What do you know about it? nothing." He also doesn't put the ring on because it makes the ring wraiths know his location, so it's less will power and more being scared of them.
There is so many of these parallels, that it's pretty obvious why people who only watched the movies, and they are a lot more than book readers, like Sam better.