[MCRmyGirl4eva]

I suppose Galadriel wanted to keep the Fellowship's unity; they were much stronger as a whole than they were apart. To accuse Boromir would have driven them farther apart than Boromir already felt. In the extended Fellowship movie, Boromir is already angry at Aragorn for not taking the Ring to Gondor, and he spits out "You were quick enough to trust the Elves! Have you so little faith in your own people?" For Aragorn to have more than his intrinsic suspicion of Boromir would have forced him to do or say something rash, and Boromir would either have gotten away with the Ring or been struck down by one of the Fellowship, both of which would have led to none of the remaining members trusting each other and causing the entire Fellowship, and thus, Middle-Earth, to fall.

Also, perhaps Galadriel saw what would have possibly happened if she had told Aragorn of what Boromir was thinking of attempting.