I'm going to post the transcript from the preceding conversation between Frodo and Sam:

SAM (to Gollum): Hey, stinker, don't go getting too far ahead.
FRODO: Why do you do that?
SAM: What?
FRODO: Call him names. Run him down all the time.
SAM: Because that's what he is, Mr. Frodo. There's naught left in him but lies and deceit. It's the Ring he wants. It's all he cares about.
FRODO: You have no idea what it did to him...what it's still doing to him. I want to help him, Sam.
SAM: Why?
FRODO: Because I have to believe he can come back.
SAM: You can't save him, Mr. Frodo.
FRODO: What do you know about it? Nothing! (Pause) I'm sorry Sam. I don't know why I said that.
SAM: I do. It's the Ring. You can't take your eyes off it. I've seen you. You're not eating. You barely sleep. It's taken hold of you, Mr. Frodo. You have to fight it!
FRODO: I know what I have to do, Sam. The Ring was entrusted to me. It's my task. Mine! My own!
SAM: Can't you hear yourself? Don't you know who you sound like?

In this conversation, Sam's lack of knowledge about the Ring manifests itself. Sam just sees Gollum as a murderer and a liar, and that he shouldn't be trusted. Frodo, as a ringbearer, is forced to see what Gollum once was, and what he has changed into. Gollum was once a hobbit-like creature, much like Frodo. And he has turned into a horrible creature. That's why Frodo must believe that Gollum can come back. Because if Gollum can't come back, then Frodo can't come back. That's why Sam's comment, "You can't save him." sets Frodo off. In Frodo's mind, Sam is essentially saying, "You can't be saved, Mr. Frodo." That's not something Frodo needed to hear. So he turns to accusing Sam of stupidity. Sam is not a ringbearer, so he can't know what it's like. Then Sam starts telling Frodo what to do ("You have to fight it!". This really ticks Frodo off. So he becomes possessive of his horrible task. Then Sam hears the "Mine! My own!" and it strikes him that Frodo sounds much like Gollum. "It came to me, my love, my love, my precious...it was my birthday present." Gollum was very possessive of the Ring, and Frodo was becoming so. This reinforces Frodo's belief that Gollum must be able to come back. Since Frodo has already started morphing into a FrodoGollum, he must believe with all his being that he can come back, or the whole thing is worthless.

Well what's great about Sam is how he DOES have an idea what it's like to hold that thing. However, he and Bilbo are the only two ring bearers to ever willingly give up the ring. Though Bilbo was kind of forced to willingly give it away. Sam, even though he used it several times and held it through Mordor, was able to give back the ring without hesitation (there was slight hesitation in the movies, but not in the books). Then there was when he desperately wanted to help Frodo destroy it, but instead of just taking it off the weakend, collapsed Frodo, like most would, he decided to just pick up Frodo himself.

"I may not be able to carry it for you, but I can carry you!"

This shows he does know what it's like to carry the ring. He knows the price. But he is able to resist it. So perhaps by saying what he did, he had no intent to insult Frodo but inform him. Maybe he knew what Frodo's reaction would be, but also knew it needed to be said.

So what he has no idea about is being unable to resist its temptation. Now while I'm sure over a long time he would've succumbed to its corruption (though less so than Bilbo over 60-some years), Frodo basically did immediately. So Sam is unique in the sense he has the ability to fight the corruption of the ring more than most others. So perhaps by saying what he did, he thought he could ultimately inspire Frodo into resisting the transformation into a Gollum, but in execution it just made him mad.

This begs the question, how different would the story have been if Sam had acquired the ring. Would Frodo have said the same thing to him? We know Sam had a MUCH stronger will. Could Frodo even carry Sam? I don't see Elijah Wood lifting Sean Astin for particularly long!! Just mindless speculation...

A complicated and perfect friendship and an obvious choice by Gandalf to rid Arda of The Ring. They needed each other and if either had failed terrible Doom would have followed. I include Seagol/Gollum in this as well.