Becky had two AoEs in her repertoire; Domain of Blue Fire and Cold Haze. She could only execute them when there were no allies around in the spell's ranger.
That's why Becky wanted Eren to prioritize her AoE execution before any of her teammates started with their moves. She couldn't control her AoEs the way she wanted to. She couldn't make her spell exclude her teammates and only affect the team's opponents.
So instead of trying to control what she couldn't, Becky wanted the team to start with her spell. In a way, her thinking was not wrong.
She wanted to cast her AoEs with peace of mind. Then she would retreat from the frontline and let her teammates take care of the remaining targets that survived her spell.
But the butcher was thinking long term. He had asked her to learn to control her AoEs. With her AoEs, it was possible. She was just lacking the motivation to do so.
