Frodo's resistance to Galadriel's mind games may play some part in that. as of the scene you are describing, Frodo had not fully experienced the torments that the ring would bring upon him and he was overconfident. When this happened, Galadriel realized that there would be no changing of Frodo's mind and so decided that she and her people would (possibly) leave Middle Earth. Since Galadriel's scrying bowl only showed what the two hobbits were thinking, and as she had seen what Sam and Frodo had seen, she had little to no faith that they could carry out their dire mission. She didn't want her people (the Galadrhrim) to suffer the fates of numerous other Elvish kingdoms, so she would leave Middle Earth rather than suffer defeat at the hands of her sworn enemy, Sauron.

I hope that answers your question!

Frodo's resistance to Galadriel's mind games may play some part in that. As of the scene you are describing, Frodo had not fully experienced the torments that the ring would bring upon him and he was overconfident. When this happened, Galadriel realized that there would be no changing of Frodo's mind and so decided that she and her people would (possibly) leave Middle Earth. 

Since Galadriel's scrying bowl only showed what the two hobbits were thinking, and as she had seen what Sam and Frodo had seen, she had little to no faith that they could carry out their dire mission. She didn't want her people (the Galadhrim) to suffer the fates of numerous other Elvish kingdoms, so she would leave Middle Earth rather than suffer defeat at the hands of her sworn enemy, Sauron.