She said that she knew that Egwene wanted to have control over Cairhien. Elayne goes on to explain that their goals are in union - if the Shadowspawn were to march against Andor, they could march through Cairhien to accomplish that. Keep in mind that if they got that far south, that wouldn't bode well for the White Tower, so Cairhien would be the closest place the White Tower could draw reinforcements from if the Borderlands failed.