I think at that point, Buffy had accepted that the amulet would have to be worn, just on the chance that it actually would be helpful, but was reluctant to put either of the only other two candidates at that additional risk, Faith because it might look like some sort of retaliation for her part in the mutiny, and Spike because of her mixed personal feelings for him (On the one hand, he was the obvious candidate, both because she trusted him totally, and she considered him to be the stronger fighter. On the other hand, she loved him, whether she was willing to admit it, even to herself, at that point, and did not want to place him at the additional risk)
On Spike's part (though this really isn't part of the question, but I believe that i should be mentioned) I am almost certain that he insisted on wearing the amulet in order to relieve Buffy of making such a decision so soon after what had happened to Xander and the Potentials at the vineyard.
Personally, I would have waited until the Potentials had all been activated and then given the damn thing to Kennedy.