Galadriel's intentions.

[Lhunardawen]

Originally Posted by lmp

I think she showed each one his own heart, and each one was tempted by what had been laid bare.

Galadriel was trying to show each of them their humanity. They are not infallible; despite oaths taken and friendships formed and the thinking that they are (insert positive trait here) enough to rise up to the task, they are still "humans" with desires and needs and weaknesses, which they would have to endure more and more as they advance in their Quest. I would say Galadriel was trying to show them the things that they could possibly value more than fulfilling their "duties" and leave them to assess themselves, whether or not they would give in to their desires.

Apparently, as their conversation later on reveals, Galadriel's testing has had an effect on each of them. For the first time in the Quest, they thought twice about their participation. "Why am I here in the first place? Is this the right thing for me to do? Can I really handle this? Would I give up the chance of a more peaceful life? What was I thinking when I chose to be part of the Fellowship?" And I believe it is in that time that they completely understood that each of them has a sense of ownership in the Fellowship. They are not merely there so that the tale of the Nine would be fulfilled. Though they cannot see it, they have a meaningful purpose for being in that group. And because of this, they would have to say no to what Galadriel has offered them. Maybe this is also why Galadriel tested them: to help them realize how important each of them are to the Fellowship.