i think the first thing you need to tell your daughter is that if she loves the birds, she should make sure that they are happy, and the easiest way to ensure that is to keep them free and out of a cage.
instead of asking her to let go, why don't you help her build a bird feeder, with grains and water for birds to come in? That way, even if she sets the birds free, they will still keep coming back, along with many more.
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Got a bun in the oven