Kwang Hee Han I know "would" is used for politeness, past habits, etc but I do not know what is the purpose of "would" here in this sentence. " Using "would" emphasizes that the person asking finds drinking onion extract undesirable/repulsive. It suggests that the person asking is doubtful that there is a good reason for it and is asking for a convincing reason.
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Kwang Hee HanI know "would" is used for politeness, past habits, etc but I do not know what is the purpose of "would" here in this sentence.If it was something nice, like a juice drink, you could simply ask "why do you drink that?"