Decapitated calf, used as atonement for murder, is forbidden for benefit and can not be used to betroth a woman - because it is compared to sacrifices, which are forbidden for benefit.
Why are the birds of a metsora forbidden for benefit? The procedure requires slaughtering one of them, then dipping the other one into blood and letting it go free. It is performed outside the city, but is compared to sacrifices inside the Temple which are prohibited for benefit. The bird which is let free is afterwards not prohibited for benefit, for the Torah would not create a stumbling block.
Eruvin 66 – Giving away
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