Using just why does not sound right to me. " But, "as to why" is perfectly correct, although I can see why it would sound strange to a non native speaker.
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sam1947I can see why it would sound strange to a non native speaker.It sounds awful to a native too.
Chloeedoes the sentence keep its meaning if I write only 'why' instead 'as to why'?No. You can't leave out "as to" in those sentences. "are puzzled why" and "I'm baffled why" won't work. Instead of "as to" you can have "about the reason", however, giving "are puzzled about the reason why" and "I'm baffled about the reason why"