Ideally, if Kyou would've fired first, the shields would've collapsed and then Asher's missiles would've done tons of damage.
But the way things went, Asher didn't get behind cover right away so his attack started sooner than Kyou's. His missiles did enough to reduce the enemy barriers to zero - Kyou's missiles by that point would be mostly wasted, so I thought it was better for her to hold on to them (ammo is limited, so I thought I was being nice).
That, by the way, would be a good thing to remember in future battles, to try and coordinate shots like that. There are some things done as a coordinated team (or a pair of characters) which will have much higher success rates than anything each of you can pull off individually.