You're not entirely correct with this.
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Neem only affects plants that actually do eat the plant - with the exception of those that you hit during spraying - they're dead. There has always been a debate about the safety of Neem with bees, as they eat pollen. In the US, it is marketed as safe for bees.
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As for spraying early or late, it is not less effective, and it has nothing to do with saving the good bugs. It is recommended to apply before or after sundown, for 2 reasons: 1) leaves should not be sprayed in full sun, as they can burn, 2) the leaf stomata are closed when the temp and light levels are lower, and therefore, will not get clogged, and prevent the plant from breathing.
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Lastly, Neem does kill flying bugs. Anything that eats the plant, as stated before. (wings or no)